Updated on 2024/02/02

写真a

 
TAKAHASHI Ryo
 
Organization
Graduate School of Mathematics Division of Mathematics Fundamental Mathematics Professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science Department of Mathematics
Title
Professor

Degree 3

  1. 博士(理学) ( 2004.3   岡山大学 ) 

  2. 修士(理学) ( 2002.3   岡山大学 ) 

  3. 学士(総合人間学) ( 2000.3   京都大学 ) 

Research Areas 1

  1. Natural Science / Algebra  / Commutative Algebra

Current Research Project and SDGs 1

  1. representation theory of commutative rings

Education 2

  1. Okayama University   Graduate School, Division of Science and Technology

    - 2004.3

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    Country: Japan

  2. Kyoto University   Faculty of Integrated Human Studies

    - 2000.3

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    Country: Japan

Professional Memberships 1

  1. 日本数学会

Awards 2

  1. MSJ Algebra Prize

    2020.3   The Mathematical Society of Japan   Subcategories of module categories of commutative rings

    Ryo Takahashi

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    Award type:Award from Japanese society, conference, symposium, etc.  Country:Japan

  2. MSJ Takebe Prize

    2004.9   The Mathematical Society of Japan  

    Ryo Takahashi

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    Award type:Award from Japanese society, conference, symposium, etc.  Country:Japan

 

Papers 124

  1. Cofiniteness of local cohomology modules and subcategories of modules

    Takahashi, R; Wakasugi, N

    COLLECTANEA MATHEMATICA     2023.11

  2. On the categorical entropy of the Frobenius pushforward functor Reviewed

    Matsui, H; Takahashi, R

    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY   Vol. 55 ( 3 ) page: 1358 - 1372   2023.6

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    Language:English  

    DOI: 10.1112/blms.12796

    Web of Science

  3. Dominant Local Rings and Subcategory Classification Reviewed

    Takahashi, R

    INTERNATIONAL MATHEMATICS RESEARCH NOTICES   Vol. 2023 ( 9 ) page: 7259 - 7318   2023.5

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    Language:English  

    DOI: 10.1093/imrn/rnac053

    Web of Science

  4. Faltings' annihilator theorem and <i>t</i>-structures of derived categories Reviewed

    Takahashi, R

    MATHEMATISCHE ZEITSCHRIFT   Vol. 304 ( 1 )   2023.5

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  5. On the subcategories of <i>n</i>-torsionfree modules and related modules Reviewed

    Dey, S; Takahashi, R

    COLLECTANEA MATHEMATICA   Vol. 74 ( 1 ) page: 113 - 132   2023.1

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  6. Auslander-Reiten conjecture and finite injective dimension of Hom Reviewed

    Dipankar Ghosh, Ryo Takahashi

    Kyoto Journal of Mathematics     2023

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    Authorship:Last author   Language:English   Publishing type:Research paper (scientific journal)  

  7. Solid generators in module categories and applications Reviewed

    Ryo Takahashi

    Rendiconti del Seminario Matematico della Università di Padova     2023

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    Authorship:Lead author, Last author, Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

  8. Remarks on complexities and entropies for singularity categories Reviewed

    R. Takahashi

    Comptes Rendus Mathématique. Académie des Sciences. Paris     2023

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    Authorship:Lead author, Last author, Corresponding author   Language:English  

  9. When is a subcategory Serre or torsionfree? Reviewed

    K.-i. Iima, H. Matsui, K. Shimada, R. Takahashi

    Publ. Res. Inst. Math. Sci.     2023

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    Authorship:Last author   Language:English   Publishing type:Research paper (scientific journal)  

  10. Maximal Cohen-Macaulay tensor products and vanishing of Ext modules Reviewed

    Kimura, K; Otake, Y; Takahashi, R

    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY   Vol. 54 ( 6 ) page: 2456 - 2468   2022.12

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    Language:English  

    DOI: 10.1112/blms.12705

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  11. Spanier-Whitehead Categories of Resolving Subcategories and Comparison with Singularity Categories Reviewed

    Bahlekeh, A; Salarian, S; Takahashi, R; Toosi, Z

    ALGEBRAS AND REPRESENTATION THEORY   Vol. 25 ( 3 ) page: 595 - 613   2022.6

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s10468-021-10037-x

    Web of Science

  12. Comparisons Between Annihilators of Tor and Ext Reviewed

    Dey, S; Takahashi, R

    ACTA MATHEMATICA VIETNAMICA   Vol. 47 ( 1 ) page: 123 - 139   2022.3

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  13. Filtrations in Module Categories, Derived Categories, and Prime Spectra Reviewed

    Matsui, H; Takahashi, R

    INTERNATIONAL MATHEMATICS RESEARCH NOTICES   Vol. 2022 ( 5 ) page: 3457 - 3492   2022.2

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    Language:English  

    DOI: 10.1093/imrn/rnaa284

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  14. ON REDUCING HOMOLOGICAL DIMENSIONS OVER NOETHERIAN RINGS Reviewed

    Araya, T; Takahashi, R

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   Vol. 150 ( 2 ) page: 469 - 480   2022.2

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    Language:English  

    DOI: 10.1090/proc/15785

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  15. Intersections of resolving subcategories and intersections of thick subcategories Reviewed

    Takahashi, R

    EUROPEAN JOURNAL OF MATHEMATICS   Vol. 7 ( 4 ) page: 1767 - 1790   2021.12

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  16. Grothendieck groups, convex cones and maximal Cohen-Macaulay points Reviewed

    Takahashi, R

    MATHEMATISCHE ZEITSCHRIFT   Vol. 299 ( 1-2 ) page: 53 - 82   2021.10

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s00209-020-02685-4

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  17. Trace ideals of canonical modules, annihilators of Ext modules, and classes of rings close to being Gorenstein Reviewed

    Dao, HL; Kobayashi, T; Takahashi, R

    JOURNAL OF PURE AND APPLIED ALGEBRA   Vol. 225 ( 9 )   2021.9

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  18. Classification of dominant resolving subcategories by moderate functions Reviewed

    Takahashi, R

    ILLINOIS JOURNAL OF MATHEMATICS   Vol. 65 ( 3 ) page: 597 - 618   2021.9

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    Language:English  

    DOI: 10.1215/00192082-9330146

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  19. Some criteria for detecting large homomorphisms of local rings Reviewed

    Gheibi, M; Takahashi, R

    COMMUNICATIONS IN ALGEBRA   Vol. 49 ( 8 ) page: 3490 - 3500   2021.7

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1080/00927872.2021.1899194

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  20. QUASI-PROJECTIVE DIMENSION Reviewed

    Gheibi, M; Jorgensen, DA; Takahashi, R

    PACIFIC JOURNAL OF MATHEMATICS   Vol. 312 ( 1 ) page: 113 - 147   2021.5

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    Language:English  

    DOI: 10.2140/pjm.2021.312.113

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  21. Homogeneous prime elements in normal two-dimensional graded rings Reviewed

    Singh, AK; Takahashi, R; Watanabe, K

    JOURNAL OF ALGEBRA   Vol. 571   page: 339 - 349   2021.4

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jalgebra.2018.07.012

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  22. The Jacobian ideal of a commutative ring and annihilators of cohomology Reviewed

    Iyengar, SB; Takahashi, R

    JOURNAL OF ALGEBRA   Vol. 571   page: 280 - 296   2021.4

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jalgebra.2018.07.034

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  23. COHOMOLOGICAL DIMENSIONS OF SPECIALIZATION-CLOSED SUBSETS AND SUBCATEGORIES OF MODULES Reviewed

    Matsui, H; Nam, TT; Takahashi, R; Tri, NM; Yen, DN

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   Vol. 149 ( 2 ) page: 481 - 496   2021.2

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1090/proc/15102

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  24. POWERS OF THE MAXIMAL IDEAL AND VANISHING OF (CO)HOMOLOGY Reviewed

    Celikbas, O; Takahashi, R

    GLASGOW MATHEMATICAL JOURNAL   Vol. 63 ( 1 ) page: 1 - 5   2021.1

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1017/S0017089519000466

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  25. Generation in module categories and derived categories of commutative rings Reviewed

    Ryo Takahashi

    Commutative algebra, Expository Papers Dedicated to David Eisenbud on the Occasion of his 75th Birthday, Springer, Cham     page: 723 - 751   2021

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    Authorship:Lead author, Last author, Corresponding author   Language:English   Publishing type:Part of collection (book)  

  26. Resolving subcategories whose finitely presented module categories are abelian Reviewed

    Takahashi, R

    COMPTES RENDUS MATHEMATIQUE   Vol. 359 ( 5 ) page: 577 - 592   2021

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    Language:English  

    DOI: 10.5802/crmath.197

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  27. Resolving Subcategories Closed Under Certain Operations and a Conjecture of Dao and Takahashi Reviewed

    Sadeghi, A; Takahashi, R

    MICHIGAN MATHEMATICAL JOURNAL   Vol. 70 ( 2 ) page: 341 - 367   2021

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    Language:English  

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  28. FLAT RING EPIMORPHISMS AND UNIVERSAL LOCALIZATIONS OF COMMUTATIVE RINGS Reviewed

    Hügel, LA; Marks, F; Stovícek, J; Takahashi, R; Vitória, J

    QUARTERLY JOURNAL OF MATHEMATICS   Vol. 71 ( 4 ) page: 1489 - 1520   2020.12

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1093/qmath/haaa041

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  29. Construction of spectra of triangulated categories and applications to commutative rings Reviewed

    Matsui, H; Takahashi, R

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   Vol. 72 ( 4 ) page: 1283 - 1307   2020.10

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.2969/jmsj/82868286

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  30. Maximal Cohen-Macaulay modules that are not locally free on the punctured spectrum Reviewed

    Kobayashi, T; Lyle, J; Takahashi, R

    JOURNAL OF PURE AND APPLIED ALGEBRA   Vol. 224 ( 7 )   2020.7

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jpaa.2020.106311

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  31. A TOPOLOGY ON THE SET OF ISOMORPHISM CLASSES OF MAXIMAL COHEN-MACAULAY MODULES Reviewed

    Hiramatsu, N; Takahashi, R

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   Vol. 148 ( 6 ) page: 2359 - 2369   2020.6

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1090/proc/14965

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  32. On the radius of the category of extensions of matrix factorizations Reviewed

    Shimada, K; Takahashi, R

    JOURNAL OF ALGEBRA   Vol. 546   page: 566 - 579   2020.3

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jalgebra.2019.10.054

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  33. Local rings with quasi-decomposable maximal ideal Reviewed

    Nasseh, S; Takahashi, R

    MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY   Vol. 168 ( 2 ) page: 305 - 322   2020.3

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1017/S0305004118000695

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  34. LITTLE DIMENSION AND THE IMPROVED NEW INTERSECTION THEOREM Reviewed

    Nakamura, T; Takahashi, R; Yassemi, S

    MATHEMATICA SCANDINAVICA   Vol. 126 ( 2 ) page: 209 - 220   2020

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.7146/math.scand.a-119740

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  35. GORENSTEIN MODIFICATIONS AND Q-GORENSTEIN RINGS Reviewed

    Dao, H; Iyama, O; Takahashi, R; Wemyss, M

    JOURNAL OF ALGEBRAIC GEOMETRY   Vol. 29 ( 4 ) page: 729 - 751   2020

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1090/jag/760

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  36. Burch ideals and Burch rings Reviewed

    Dao, HL; Kobayashi, T; Takahashi, R

    ALGEBRA & NUMBER THEORY   Vol. 14 ( 8 ) page: 2121 - 2150   2020

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    DOI: 10.2140/ant.2020.14.2121

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  37. Generation in singularity categories of hypersurfaces of countable representation type Reviewed

    Araya, T; Iima, K; Ono, M; Takahashi, R

    ARCHIV DER MATHEMATIK   Vol. 113 ( 6 ) page: 603 - 615   2019.12

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s00013-019-01374-x

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  38. Rings whose ideals are isomorphic to trace ideals Reviewed

    Kobayashi, T; Takahashi, R

    MATHEMATISCHE NACHRICHTEN   Vol. 292 ( 10 ) page: 2252 - 2261   2019.10

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1002/mana.201800309

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  39. ON THE IDEAL CASE OF A CONJECTURE OF HUNEKE AND WIEGAND Reviewed

    Celikbas, O; Goto, S; Takahashi, R; Taniguchi, N

    PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY   Vol. 62 ( 3 ) page: 847 - 859   2019.8

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1017/S0013091518000731

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  40. ON THE SECOND RIGIDITY THEOREM OF HUNEKE AND WIEGAND Reviewed

    Celikbas, O; Takahashi, R

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   Vol. 147 ( 7 ) page: 2733 - 2739   2019.7

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1090/proc/14564

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  41. On the transitivity of degeneration of modules Reviewed

    Takahashi, R

    MANUSCRIPTA MATHEMATICA   Vol. 159 ( 3-4 ) page: 431 - 444   2019.7

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s00229-018-1076-2

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  42. Ulrich modules over Cohen-Macaulay local rings with minimal multiplicity Reviewed

    Kobayashi, T; Takahashi, R

    QUARTERLY JOURNAL OF MATHEMATICS   Vol. 70 ( 2 ) page: 487 - 507   2019.6

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1093/qmath/hay055

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  43. Degenerations over (<i>A</i><sub>∞</sub>)-singularities and construction of degenerations over commutative rings Reviewed

    Hiramatsu, N; Takahashi, R; Yoshino, Y

    JOURNAL OF ALGEBRA   Vol. 525   page: 374 - 389   2019.5

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jalgebra.2018.12.031

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  44. Remarks on dimensions of triangulated categories Reviewed

    Aihara, T; Takahashi, R

    JOURNAL OF ALGEBRA   Vol. 521   page: 235 - 246   2019.3

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jalgebra.2018.12.001

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  45. Openness of the Regular Locus and Generators for Module Categories Reviewed

    Iyengar, SB; Takahashi, R

    ACTA MATHEMATICA VIETNAMICA   Vol. 44 ( 1 ) page: 207 - 212   2019.3

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s40306-018-0294-8

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  46. Applications and homological properties of local rings with decomposable maximal ideals Reviewed

    Nasseh, S; Sather-Wagstaff, S; Takahashi, R; VandeBogert, K

    JOURNAL OF PURE AND APPLIED ALGEBRA   Vol. 223 ( 3 ) page: 1272 - 1287   2019.3

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jpaa.2018.06.006

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  47. Totally reflexive modules and Poincare series Reviewed

    Gheibi, M; Takahashi, R

    JOURNAL OF ALGEBRA   Vol. 520   page: 440 - 459   2019.2

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jalgebra.2018.10.040

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  48. Noncommutative resolutions using syzygies Reviewed

    Dao, H; Iyama, O; Iyengar, SB; Takahashi, R; Wemyss, M; Yoshino, Y

    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY   Vol. 51 ( 1 ) page: 43 - 48   2019.2

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1112/blms.12210

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  49. ASSOCIATED PRIMES AND SYZYGIES OF LINKED MODULES Reviewed

    Celikbas, O; Dibaei, MT; Gheibi, M; Sadeghi, A; Takahashi, R

    JOURNAL OF COMMUTATIVE ALGEBRA   Vol. 11 ( 3 ) page: 301 - 323   2019

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1216/JCA-2019-11-3-301

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  50. Two generalizations of Auslander-Reiten duality and applications Reviewed

    Arash Sadeghi, Ryo Takahashi

      Vol. 63   page: 335-351   2019

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  51. ON THE VANISHING OF SELF EXTENSIONS OVER COHEN-MACAULAY LOCAL RINGS Reviewed

    Araya, T; Celikbas, O; Sadeghi, A; Takahashi, R

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   Vol. 146 ( 11 ) page: 4563 - 4570   2018.11

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1090/proc/13944

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  52. Structure of Irreducible Homomorphisms to/from Free Modules Reviewed

    Nasseh, S; Takahashi, R

    ALGEBRAS AND REPRESENTATION THEORY   Vol. 21 ( 2 ) page: 471 - 485   2018.4

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s10468-017-9722-z

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  53. On the ideal case of a conjecture of Auslander and Reiten Reviewed

    Celikbas, O; Iima, K; Sadeghi, A; Takahashi, R

    BULLETIN DES SCIENCES MATHEMATIQUES   Vol. 142   page: 94 - 107   2018.2

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.bulsci.2017.09.005

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  54. Thick tensor ideals of right bounded derived categories of commutative rings Reviewed

    Takahashi, R

    REPRESENTATIONS OF ALGEBRAS   Vol. 705   page: 225 - 250   2018

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    Language:English   Publishing type:Part of collection (book)  

    DOI: 10.1090/conm/705/14193

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  55. THICK SUBCATEGORIES OVER ISOLATED SINGULARITIES Reviewed

    Takahashi, R

    PACIFIC JOURNAL OF MATHEMATICS   Vol. 291 ( 1 ) page: 183 - 211   2017.11

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.2140/pjm.2017.291.183

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  56. ON THE AUSLANDER-REITEN CONJECTURE FOR COHEN MACAULAY LOCAL RINGS Reviewed

    Goto, S; Takahashi, R

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   Vol. 145 ( 8 ) page: 3289 - 3296   2017.8

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1090/proc/13487

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  57. When are -syzygy modules -torsionfree? Reviewed

    Matsui, H; Takahashi, R; Tsuchiya, Y

    ARCHIV DER MATHEMATIK   Vol. 108 ( 4 ) page: 351 - 355   2017.4

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s00013-017-1020-9

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  58. Singularity categories and singular equivalences for resolving subcategories Reviewed

    Matsui, H; Takahashi, R

    MATHEMATISCHE ZEITSCHRIFT   Vol. 285 ( 1-2 ) page: 251 - 286   2017.2

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s00209-016-1706-x

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  59. Thick tensor ideals of right bounded derived categories Reviewed

    Matsui, H; Takahashi, R

    ALGEBRA & NUMBER THEORY   Vol. 11 ( 7 ) page: 1677 - 1738   2017

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    DOI: 10.2140/ant.2017.11.1677

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  60. Ulrich ideals and almost Gorenstein rings Reviewed

    Shiro Goto, Ryo Takahashi, Naoki Taniguchi

      Vol. 144   page: 2811-2823   2016

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  61. Annihilation of cohomology, generation of modules and finiteness of derived dimension Reviewed

    Abdolnaser Bahlekeh, Ehsan Hakimian, Shokrollah Salarian, Ryo Takahashi

      Vol. 67   page: 387-404   2016

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  62. Ulrich ideals and modules over two-dimensional rational singularities Reviewed

    Shiro Goto, Kazuho Ozeki, Ryo Takahashi, Kei-ichi Watanabe, Ken-ichi Yoshida

      Vol. 221   page: 69-110   2016

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  63. Extension closedness of syzygies and local Gorensteinness of commutative rings Reviewed

    Shiro Goto, Ryo Takahashi

      Vol. 19   page: 511-521   2016

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  64. Perfect linkage of Cohen-Macaulay modules over Cohen-Macaulay rings Reviewed

    Kei-ichiro Iima, Ryo Takahashi

      Vol. 458   page: 134-155   2016

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  65. Annihilation of cohomology and strong generation of module categories Reviewed

    Srikanth B. Iyengar, Ryo Takahashi

    International Mathematics Research Notices. IMRN   Vol. 2016   page: 499-535   2016

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  66. Huneke-Wiegand conjecture and change of rings Reviewed

    Shiro Goto, Ryo Takahashi, Naoki Taniguchi, Hoang Le Truong

    J. Algebra   Vol. 422   page: 33-52   2015

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  67. The dimension of a subcategory of modules Reviewed

    Hailong Dao, Ryo Takahashi

    Forum of Mathematics. Sigma   Vol. 3   2015

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    Authorship:Last author   Language:English   Publishing type:Research paper (scientific journal)  

  68. Generators and dimensions of derived categories of modules Reviewed

    Takuma Aihara, Ryo Takahashi

    Communications in Algebra   Vol. 43   page: 5003-5029   2015

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  69. Endofunctors of singularity categories characterizing Gorenstein rings Reviewed

    Takuma Aihara, Ryo Takahashi

    Proceedings of the American Mathematical Society   Vol. 143   page: 3777-3779   2015

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  70. Non-commutative resolutions and Grothendieck groups Reviewed

    Hailong Dao, Osamu Iyama, Ryo Takahashi, Charles Vial

    J. Noncommut. Geom.   Vol. 9   page: 21-34   2015

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  71. Maximal Cohen-Macaulay approximations and Serre's condition Reviewed

    Hiroki Matsui, Ryo Takahashi

    Acta Math. Vietnam.   Vol. 40   page: 197-203   2015

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    Authorship:Last author, Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

  72. Building modules from the singular locus Reviewed

    Jesse Burke, Lars Winther Christensen, Ryo Takahashi

    Math. Scand.   Vol. 116   page: 23-33   2015

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  73. Upper bounds for dimensions of singularity categories Reviewed

    Hailong Dao, Ryo Takahashi

    C. R. Math. Acad. Sci. Paris   Vol. 353   page: 297-301   2015

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  74. Almost Gorenstein rings -- towards a theory of higher dimension -- Reviewed

    Shiro Goto, Ryo Takahashi, Naoki Taniguchi

    J. Pure Appl. Algebra   Vol. 219   page: 2666-2712   2015

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    Language:English   Publishing type:Research paper (scientific journal)  

  75. Bounds on depth of tensor products of modules Reviewed

    Olgur Celikbas, Arashi Sadeghi, Ryo Takahashi

    J. Pure Appl. Algebra   Vol. 219   page: 1670-1684   2015

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  76. Classification of resolving subcategories and grade consistent functions Reviewed

    Hailong Dao, Ryo Takahashi

    Int. Math. Res. Not. IMRN   Vol. 2015   page: 119-149   2015

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  77. Modules that detect finite homological dimensions Reviewed

    Olgur Celikbas, Hailong Dao, Ryo Takahashi

    Kyoto J. Math.   Vol. 54 ( 2 ) page: 295-310   2014

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  78. Brauer-Thrall for totally reflexive modules over local rings of higher dimension Reviewed

    Olgur Celikbas, Mohsen Gheibi, Ryo Takahashi

    Algebr. Represent. Theory   Vol. 17 ( 3 ) page: 997-1008   2014

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  79. Reconstruction from Koszul homology and applications to module and derived categories Reviewed

    Ryo Takahashi

    Pacific J. Math.   Vol. 268 ( 1 ) page: 231-248   2014

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  80. The radius of a subcategory of modules Reviewed

    Hailong Dao, Ryo Takahashi

    Algebra Number Theory   Vol. 8 ( 1 ) page: 141-172   2014

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  81. Dimensions of triangulated categories with respect to subcategories Reviewed

    Takuma Aihara, Tokuji Araya, Osamu Iyama, Ryo Takahashi, Michio Yoshiwaki

    J. Algebra   Vol. 399   page: 205-219   2014

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  82. Ulrich ideals and modules Reviewed

    Shiro Goto, Kazuho Ozeki, Ryo Takahashi, Kei-ichi Watanabe, Ken-ichi Yoshida

    Math. Proc. Cambridge Philos. Soc.   Vol. 156 ( 1 ) page: 137-166   2014

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  83. Annihilation of cohomology and decompositions of derived categories Reviewed

    Srikanth B. Iyengar, Ryo Takahashi

    Homology, Homotopy Appl.   Vol. 16 ( 2 ) page: 231-237   2014

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  84. Classifying resolving subcategories over a Cohen-Macaulay local ring Reviewed

    Ryo Takahashi

    Math. Z.   Vol. 273 ( 1 ) page: 569-587   2013

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  85. Thick subcategories over Gorenstein local rings that are locally hypersurfaces on the punctured spectra Reviewed

    Ryo Takahashi

    J. Math. Soc. Japan   Vol. 65 ( 2 ) page: 357-374   2013

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  86. Tilting and cluster tilting for quotient singularities Reviewed

    Osamu Iyama, Ryo Takahashi

    Math. Ann.   Vol. 356 ( 3 ) page: 1065-1105   2013

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  87. Auslander-Reiten conjecture and Auslander-Reiten duality Reviewed

    O. Celikbas, R. Takahashi

    J. Algebra   Vol. 382   page: 100-114   2013

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  88. On the left perpendicular category of the modules of finite projective dimension Reviewed

    Tokuji Araya, Kei-ichiro Iima, Ryo Takahashi

    Comm. Algebra   Vol. 40 ( 8 ) page: 2693-2699   2012

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  89. On the structure of Cohen-Macaulay modules over hypersurfaces of countable Cohen-Macaulay representation type Reviewed

    T. Araya, K.-i. Iima, R. Takahashi

    J. Algebra   Vol. 361   page: 213-224   2012

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  90. Contravariantly finite resolving subcategories over commutative rings Reviewed

    R. Takahashi

    Amer. J. Math.   Vol. 133 ( 2 ) page: 417-436   2011

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  91. When is there a nontrivial extension-closed subcategory? Reviewed

    R. Takahashi

    J. Algebra   Vol. 331 ( 1 ) page: 388-399   2011

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  92. Homological aspects of semidualizing modules Reviewed

    R. Takahashi, D. White

    Math. Scand.   Vol. 106 ( 1 ) page: 5-22   2010

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  93. On the existence of embeddings into modules of finite homological dimensions Reviewed

    R. Takahashi, S. Yassemi, Y. Yoshino

    Proc. Amer. Math. Soc.   Vol. 138 ( 7 ) page: 2265-2268   2010

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  94. Classifying thick subcategories of the stable category of Cohen-Macaulay modules Reviewed

    R. Takahashi

    Adv. Math.   Vol. 225 ( 4 ) page: 2076-2116   2010

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  95. On localizing subcategories of derived categories Reviewed

    R. Takahashi

    J. Math. Kyoto Univ.   Vol. 49 ( 4 ) page: 771-783   2009

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  96. Local cohomology based on a nonclosed support defined by a pair of ideals Reviewed

    R. Takahashi, Y. Yoshino, T. Yoshizawa

    J. Pure Appl. Algebra   Vol. 213 ( 4 ) page: 582-600   2009

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  97. Modules in resolving subcategories which are free on the punctured spectrum Reviewed

    R. Takahashi

    Pacific J. Math.   Vol. 241 ( 2 ) page: 347-367   2009

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  98. A generalization of a theorem of Foxby Reviewed

    T. Araya, R. Takahashi

    Arch. Math. (Basel)   Vol. 93 ( 2 ) page: 123-127   2009

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  99. Classifying subcategories of modules over a commutative noetherian ring Reviewed

    R. Takahashi

    J. Lond. Math. Soc. (2)   Vol. 78 ( 3 ) page: 767-782   2008

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  100. Quasi-socle ideals in a Gorenstein local ring Reviewed

    S. Goto, R. Takahashi, N. Matsuoka

    J. Pure Appl. Algebra   Vol. 212 ( 5 ) page: 969-980   2008

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  101. Direct summands of syzygy modules of the residue class field Reviewed

    R. Takahashi

    Nagoya Math. J.   Vol. 189   page: 1-25   2008

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  102. D-modules over rings with finite F-representation type Reviewed

    S. Takagi, R. Takahashi

    Math. Res. Lett.   Vol. 15 ( 3 ) page: 563-581   2008

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  103. Finite Gorenstein representation type implies simple singularity Reviewed

    L. W. Christensen, G. Piepmeyer, J. Striuli, R. Takahashi

    Adv. Math.   Vol. 218 ( 4 ) page: 1012-1026   2008

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  104. On vanishing of certain Ext modules Reviewed

    S. Goto, F. Hayasaka, R. Takahashi

    J. Math. Soc. Japan   Vol. 60 ( 4 ) page: 1045-1064   2008

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  105. On G-regular local rings Reviewed

    R. Takahashi

    Comm. Algebra   Vol. 36 ( 12 ) page: 4472-4491   2008

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  106. An uncountably infinite number of indecomposable totally reflexive modules Reviewed

    R. Takahashi

    Nagoya Math. J.   Vol. 187   page: 35-48   2007

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  107. A new approximation theory which unifies spherical and Cohen-Macaulay approximations Reviewed

    R. Takahashi

    J. Pure Appl. Algebra   Vol. 208 ( 2 ) page: 617-634   2007

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  108. On the number of indecomposable totally reflexive modules Reviewed

    R. Takahashi

    Bull. London Math. Soc.   Vol. 39 ( 3 ) page: 487-492   2007

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  109. Totally reflexive modules constructed from smooth projective curves of genus g >= 2 Reviewed

    R. Takahashi, K.-i. Watanabe

    Arch. Math. (Basel)   Vol. 89 ( 1 ) page: 60-67   2007

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  110. A characterization of modules locally of finite injective dimension Reviewed

    R. Takahashi

    Proc. Amer. Math. Soc.   Vol. 135 ( 11 ) page: 3461-3464   2007

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  111. Openness of FID-loci Reviewed

    R. Takahashi

    Glasg. Math. J.   Vol. 48 ( 3 ) page: 431-435   2006

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  112. Syzygy modules with semidualizing or G-projective summands Reviewed

    R. Takahashi

    J. Algebra   Vol. 295 ( 1 ) page: 179-194   2006

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  113. A note on a theorem of F. Wang and G. Tang Reviewed

    R. Takahashi

    Bull. Austral. Math. Soc.   Vol. 73   page: 293-297   2006

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  114. Remarks on modules approximated by G-projective modules Reviewed

    R. Takahashi

    J. Algebra   Vol. 301 ( 2 ) page: 748-780   2006

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  115. The existence of finitely generated modules of finite Gorenstein injective dimension Reviewed

    R. Takahashi

    Proc. Amer. Math. Soc.   Vol. 134 ( 11 ) page: 3115-3121   2006

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  116. On the category of modules of Gorenstein dimension zero Reviewed

    R. Takahashi

    Math. Z.   Vol. 251 ( 2 ) page: 249-256   2005

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  117. Homological invariants associated to semi-dualizing bimodules Reviewed

    T. Araya, R. Takahashi, Y. Yoshino

    J. Math. Kyoto Univ.   Vol. 45 ( 2 ) page: 287-306   2005

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  118. Modules of G-dimension zero over local rings of depth two Reviewed

    R. Takahashi

    Illinois J. Math.   Vol. 48 ( 3 ) page: 945-952   2004

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  119. Upper complete intersection dimension relative to a local homomorphism Reviewed

    R. Takahashi

    Tokyo J. Math.   Vol. 27 ( 1 ) page: 209-219   2004

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  120. On the category of modules of Gorenstein dimension zero II Reviewed

    R. Takahashi

    J. Algebra   Vol. 278 ( 1 ) page: 402-410   2004

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  121. Characterizing Cohen-Macaulay local rings by Frobenius maps Reviewed

    R. Takahashi, Y. Yoshino

    Proc. Amer. Math. Soc.   Vol. 132 ( 11 ) page: 3177-3187   2004

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  122. Some characterizations of Gorenstein local rings in terms of G-dimension Reviewed

    R. Takahashi

    Acta Math. Hungar.   Vol. 104 ( 4 ) page: 315-322   2004

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  123. Upper Cohen-Macaulay dimension Reviewed

    T. Araya, R. Takahashi, Y. Yoshino

    Math. J. Okayama Univ.   Vol. 46   page: 17-30   2004

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  124. Nagata criterion for Serre's (Rn) and (Sn)-conditions Reviewed

    R. Takahashi

    Math. J. Okayama Univ.   Vol. 41   page: 37-43   1999

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KAKENHI (Grants-in-Aid for Scientific Research) 6

  1. 各種の関数と次元による可換環の導来圏の研究

    Grant number:23K03070  2023.4 - 2026.3

    科学研究費助成事業  基盤研究(C)

    高橋 亮

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    Authorship:Principal investigator 

    Grant amount:\4680000 ( Direct Cost: \3600000 、 Indirect Cost:\1080000 )

    圏(集合のようなもの)が与えられたとき、それの充満部分圏(部分集合のようなもの)のうち適切な条件をみたすものをすべて分類する・決定するという問題が考えられる。これは、数学の複数の分野にまたがって60年以上にわたり多くの研究者によって調べられてきた重要な問題である。本研究は、可換Noether環上の有限生成加群の有界複体全体のなす導来圏という特定の圏に対してこの問題を考察することを目的とする。

  2. Generation problems in module categories and derived categories of commutative noetherian rings

    Grant number:19K03443  2019.4 - 2023.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Authorship:Principal investigator 

    Grant amount:\4290000 ( Direct Cost: \3300000 、 Indirect Cost:\990000 )

  3. Generation problems of subcategories of the module category of a Cohen-Macaulay local ring(Fostering Joint International Research)

    Grant number:16KK0099  2017 - 2019

    Fund for the Promotion of Joint International Research (Fostering Joint International Research)

    Takahashi Ryo

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    Authorship:Principal investigator 

    Grant amount:\13260000 ( Direct Cost: \10200000 、 Indirect Cost:\3060000 )

    Various results are obtained. In particular, many properties of the structure of Cohen-Macaulay modules are clarified. A Cohen-Macaulay local ring is said to have finite CM+ representation type if there are only finitely many indecomposable Cohen-Macaulay modules whose nonfree loci have positive dimension. For a Gorenstein ring of dimension one, it is proved that having finite CM+ representation type is equivalent to having either an isolated singularity or countable CM representation type. Consider the Grothendieck group of finitely generated modules modulo the subgroup spanned by pseudo-zero modules. Tensor the real number field and consider the convex cone spanned by Cohen-Macaulay modules. Various topological properties on this convex cone are obtained.

  4. 整環の表現論の総合的研究

    Grant number:16H03923  2016.4 - 2021.3

    科学研究費助成事業  基盤研究(B)

    伊山 修, 高橋 亮, 毛利 出

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    Authorship:Coinvestigator(s) 

    埴原と共同(arXiv:2209.14090)で、次数付きGorenstein環Rと有限次元代数Aに対し、Rの次数付き特異圏とAの導来圏の同値から、Rの特異圏とAの団圏の同値が得られることを示し、種々の先行研究を統一的に説明した。
    木村と共同(2106.00469, 2303.02928)で(一般には非可換)ネター代数上の加群圏の分類理論を構築した。ねじれ自由類とSerre部分圏を分類し、いくつかの特別な場合にねじれ類を分類した。
    Chan, Marczinzikと共同(2210.06180)で、dominantと呼ばれるAuslander正則環のクラスを導入し、mixed団傾加群による特徴付けを与え、さらにKoszul双対性で閉じていることを示した。Marczinzikと共同(Adv. Math.2022)で、有限束Pに対し、Pの隣接代数AがAuslander正則環であることとPが分配束であることの同値性を示した。Chan, Darpoe, Marczinzikと共同(2012.11927)で、有限次元代数Aの自明拡大代数が周期的であることと、Aの導来圏が分数的Calabi-Yauであることの同値性を示した。
    青木, 東谷, 加瀬, 水野と共同(2203.15213)で、有限次元代数の実Grothendieck群内に定まるg扇の基礎理論を構築した。ランク2の完備なg扇は符号同一性で特徴付けられることを示した(2301.01498)。淺井と共同(2112.14908)で、有限次元代数Aの実Grothendieck群に対し、標準分解から定まる錐の内点は全てTF同値であることを示し、Aが遺伝的またはE-tameの場合には錐の内部が一つの同値類であることを示した。Williamsと共同(2208.12957)で、A型前射影代数の2項準傾複体とprismの三角形分割の一対一対応を与えた。
    令和2年度が最終年度であるため、記入しない。
    令和2年度が最終年度であるため、記入しない。

  5. Thick subcategories and dimensions of derived categories of commutative rings

    Grant number:16K05098  2016.4 - 2020.3

    Takahashi Ryo

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    Authorship:Principal investigator 

    Grant amount:\4550000 ( Direct Cost: \3500000 、 Indirect Cost:\1050000 )

    The thick subcategories of the singularity category of a local ring with quasi-decomposable maximal ideal are completely classified. The cocompactly generated thick tensor ideals of the right bounded derived category of finitely generated modules over a commutative noetherian ring are completely classified. For the stable category of Cohen-Macaulay modules over an Iwanaga Gorenstein isolated singularity, being locally finite and having finite representation type turn out to be equivalent. It turns out to hold that if a finitely generated Krull-Schmidt triangulated category is locally finite, then it has dimension zero, and the converse is true if it is Ext-finite. It is found out that the residue field of a local hypersurface of countable representation type has level at most one with respect to each nonzero object.

  6. Foundations of rigid geometry from birational viewpoint

    Grant number:15H03607  2015.4 - 2019.3

    FUJIWARA KAZUHIRO

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    Authorship:Other 

    Aimed for establishing foundational aspects of rigid geometry, "Foundations of rigid geometry I" (joint with F. Kato at titech) was published from EMS (2018). A new aspect, i.e., spectral theory of filtered rings, is added during the project. Also, perfectoid spaces, which have close connection to rigid geometry, are put into our plan. After P. Scholze's introduction, many applications of perfectoid spaces are known up to now. The principal investigator has tried to understand phenomena behind cohomological purity conjectures from perfectoid viewpoint, and has given a new proof of the absolute purity conjecture.

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