Updated on 2022/10/27

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 119

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

    Kimura Kaito, Otake Yuya, Takahashi Ryo

    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY     2022.7

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    Language:Japanese  

    DOI: 10.1112/blms.12705

    Web of Science

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

    Bahlekeh Abdolnaser, Salarian Shokrollah, Takahashi Ryo, Toosi Zahra

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

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

    DOI: 10.1007/s10468-021-10037-x

    Web of Science

  3. Dominant Local Rings and Subcategory Classification

    Takahashi Ryo

    INTERNATIONAL MATHEMATICS RESEARCH NOTICES     2022.3

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    Language:Japanese  

    DOI: 10.1093/imrn/rnac053

    Web of Science

  4. Comparisons Between Annihilators of Tor and Ext Reviewed

    Dey Souvik, Takahashi Ryo

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

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  5. Filtrations in Module Categories, Derived Categories, and Prime Spectra

    Matsui Hiroki, Takahashi Ryo

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

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    Language:Japanese  

    DOI: 10.1093/imrn/rnaa284

    Web of Science

  6. ON REDUCING HOMOLOGICAL DIMENSIONS OVER NOETHERIAN RINGS Reviewed

    Araya Tokuji, Takahashi Ryo

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

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    Language:Japanese  

    DOI: 10.1090/proc/15785

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

    Dipankar Ghosh, Ryo Takahashi

    Kyoto Journal of Mathematics     2022

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

  8. Solid generators in module categories and applications Reviewed

    Ryo Takahashi

    Rendiconti del Seminario Matematico della Università di Padova     2022

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

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

    Takahashi Ryo

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

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

    DOI: 10.1007/s40879-021-00470-z

    Web of Science

  10. On the subcategories of n-torsionfree modules and related modules Reviewed

    Dey Souvik, Takahashi Ryo

    COLLECTANEA MATHEMATICA     2021.10

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

    Takahashi Ryo

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

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

    DOI: 10.1007/s00209-020-02685-4

    Web of Science

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

    Dao Hailong, Kobayashi Toshinori, Takahashi Ryo

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

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  13. Classification of dominant resolving subcategories by moderate functions

    Takahashi Ryo

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

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    Language:Japanese  

    DOI: 10.1215/00192082-9330146

    Web of Science

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

    Gheibi Mohsen, Takahashi Ryo

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

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

    DOI: 10.1080/00927872.2021.1899194

    Web of Science

  15. QUASI-PROJECTIVE DIMENSION Reviewed

    Gheibi Mohsen, Jorgensen David A., Takahashi Ryo

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

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    Language:Japanese  

    DOI: 10.2140/pjm.2021.312.113

    Web of Science

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

    Singh Anurag K., Takahashi Ryo, Watanabe Kei-ichi

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

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

    DOI: 10.1016/j.jalgebra.2018.07.012

    Web of Science

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

    Iyengar Srikanth B., Takahashi Ryo

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

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

    DOI: 10.1016/j.jalgebra.2018.07.034

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

    Matsui Hiroki, Tran Tuan Nam, Takahashi Ryo, Nguyen Minh Tri, Do Ngoc Yen

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

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

    DOI: 10.1090/proc/15102

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

    Celikbas Olgur, Takahashi Ryo

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

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

    DOI: 10.1017/S0017089519000466

    Web of Science

  20. 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)  

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

    Sadeghi Arash, Takahashi Ryo

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

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    Language:Japanese  

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

    Takahashi Ryo

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

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    Language:Japanese  

    DOI: 10.5802/crmath.197

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

    Hugel Lidia Angeleri, Marks Frederik, Stovicek Jan, Takahashi Ryo, Vitoria Jorge

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

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

    DOI: 10.1093/qmath/haaa041

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

    Matsui Hiroki, Takahashi Ryo

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

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

    DOI: 10.2969/jmsj/82868286

    Web of Science

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

    Kobayashi Toshinori, Lyle Justin, Takahashi Ryo

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

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

    DOI: 10.1016/j.jpaa.2020.106311

    Web of Science

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

    Hiramatsu Naoya, Takahashi Ryo

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

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

    DOI: 10.1090/proc/14965

    Web of Science

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

    Shimada Kaori, Takahashi Ryo

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

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

    DOI: 10.1016/j.jalgebra.2019.10.054

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  28. Local rings with quasi-decomposable maximal ideal Reviewed

    Nasseh Saeed, Takahashi Ryo

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

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

    DOI: 10.1017/S0305004118000695

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  29. GORENSTEIN MODIFICATIONS AND Q-GORENSTEIN RINGS Reviewed

    Dao Hailong, Iyama Osamu, Takahashi Ryo, Wemyss Michael

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

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

    DOI: 10.1090/jag/760

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  30. Burch ideals and Burch rings Reviewed

    Dao Hailong, Kobayashi Toshinori, Takahashi Ryo

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

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

    DOI: 10.2140/ant.2020.14.2121

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  31. LITTLE DIMENSION AND THE IMPROVED NEW INTERSECTION THEOREM Reviewed

    Nakamura Tsutomu, Takahashi Ryo, Yassemi Siamak

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

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    DOI: 10.7146/math.scand.a-119740

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

    Araya Tokuji, Iima Kei-ichiro, Ono Maiko, Takahashi Ryo

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

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

    DOI: 10.1007/s00013-019-01374-x

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  33. Rings whose ideals are isomorphic to trace ideals Reviewed

    Kobayashi Toshinori, Takahashi Ryo

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

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

    DOI: 10.1002/mana.201800309

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

    Celikbas Olgur, Goto Shiro, Takahashi Ryo, Taniguchi Naoki

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

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

    DOI: 10.1017/S0013091518000731

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

    Celikbas Olgur, Takahashi Ryo

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

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

    DOI: 10.1090/proc/14564

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  36. On the transitivity of degeneration of modules Reviewed

    Takahashi Ryo

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

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

    DOI: 10.1007/s00229-018-1076-2

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

    Kobayashi Toshinori, Takahashi Ryo

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

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

    DOI: 10.1093/qmath/hay055

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  38. Degenerations over (A(infinity))-singularities and construction of degenerations over commutative rings Reviewed

    Hiramatsu Naoya, Takahashi Ryo, Yoshino Yuji

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

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

    DOI: 10.1016/j.jalgebra.2018.12.031

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  39. Remarks on dimensions of triangulated categories Reviewed

    Aihara Takuma, Takahashi Ryo

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

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

    DOI: 10.1016/j.jalgebra.2018.12.001

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

    Nasseh Saeed, Sather-Wagstaff Sean, Takahashi Ryo, VandeBogert Keller

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

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

    DOI: 10.1016/j.jpaa.2018.06.006

    Web of Science

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

    Iyengar Srikanth B., Takahashi Ryo

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

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

    DOI: 10.1007/s40306-018-0294-8

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  42. Totally reflexive modules and Poincare series Reviewed

    Gheibi Mohsen, Takahashi Ryo

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

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    DOI: 10.1016/j.jalgebra.2018.10.040

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  43. Noncommutative resolutions using syzygies Reviewed

    Dao Hailong, Iyama Osamu, Iyengar Srikanth B., Takahashi Ryo, Wemyss Michael, Yoshino Yuji

    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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  44. ASSOCIATED PRIMES AND SYZYGIES OF LINKED MODULES Reviewed

    Celikbas Olgur, Dibaei Mohammad T., Gheibi Mohsen, Sadeghi Arash, Takahashi Ryo

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

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

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

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

    Arash Sadeghi, Ryo Takahashi

      Vol. 63   page: 335-351   2019

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

    Araya Tokuji, Celikbas Olgur, Sadeghi Arash, Takahashi Ryo

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

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

    DOI: 10.1090/proc/13944

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

    Nasseh Saeed, Takahashi Ryo

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

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

    DOI: 10.1007/s10468-017-9722-z

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

    Celikbas Olgur, Iima Kei-ichiro, Sadeghi Arash, Takahashi Ryo

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

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

    DOI: 10.1016/j.bulsci.2017.09.005

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

    Takahashi Ryo

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

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

    DOI: 10.1090/conm/705/14193

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  50. THICK SUBCATEGORIES OVER ISOLATED SINGULARITIES Reviewed

    Takahashi Ryo

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

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

    DOI: 10.2140/pjm.2017.291.183

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

    Goto Shiro, Takahashi Ryo

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

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    DOI: 10.1090/proc/13487

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  52. When are n-syzygy modules n-torsionfree? Reviewed

    Matsui Hiroki, Takahashi Ryo, Tsuchiya Yoshinao

    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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  53. Singularity categories and singular equivalences for resolving subcategories Reviewed

    Matsui Hiroki, Takahashi Ryo

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

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

    DOI: 10.1007/s00209-016-1706-x

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  54. Thick tensor ideals of right bounded derived categories Reviewed

    Matsui Hiroki, Takahashi Ryo

    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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  55. Ulrich ideals and almost Gorenstein rings Reviewed

    Shiro Goto, Ryo Takahashi, Naoki Taniguchi

      Vol. 144   page: 2811-2823   2016

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  56. 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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  57. 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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  58. 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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  59. 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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  60. 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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  61. 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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  62. The dimension of a subcategory of modules Reviewed

    Hailong Dao, Ryo Takahashi

    Forum of Mathematics. Sigma   Vol. 3   2015

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  63. 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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  64. 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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  65. 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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  66. 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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  67. 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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  68. 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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  69. 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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  70. 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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  71. 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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  72. 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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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

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

  74. 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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  75. 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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  76. 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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  77. 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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  78. 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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  79. 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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  80. 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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  81. 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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  82. Auslander-Reiten conjecture and Auslander-Reiten duality Reviewed

    O. Celikbas, R. Takahashi

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

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  83. 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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  84. 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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  85. Contravariantly finite resolving subcategories over commutative rings Reviewed

    R. Takahashi

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

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

    R. Takahashi

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

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  87. Homological aspects of semidualizing modules Reviewed

    R. Takahashi, D. White

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

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  88. 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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  89. 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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  90. On localizing subcategories of derived categories Reviewed

    R. Takahashi

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

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  91. 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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  92. 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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  93. 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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  94. 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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  95. 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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  96. 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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  97. 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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  98. 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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  99. 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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  100. On G-regular local rings Reviewed

    R. Takahashi

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

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  101. 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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  102. 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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  103. 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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  104. 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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  105. 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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  106. Syzygy modules with semidualizing or G-projective summands Reviewed

    R. Takahashi

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

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  107. 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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  108. Remarks on modules approximated by G-projective modules Reviewed

    R. Takahashi

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

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  109. 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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  110. Openness of FID-loci Reviewed

    R. Takahashi

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

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  111. 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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  112. 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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  113. 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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  114. 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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  115. 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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  116. 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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  117. 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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  118. 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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  119. 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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▼display all

KAKENHI (Grants-in-Aid for Scientific Research) 5

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

    Grant number:19K03443  2019.4 - 2022.3

    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 )

  2. 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.

  3. 整環の表現論の総合的研究

    Grant number:16H03923  2016.4 - 2021.3

    伊山 修

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    Authorship:Coinvestigator(s) 

    自然数dに対し[-d]をSerre関手に持つ三角圏を(-d)-Calabi-Yauと呼ぶが, 団圏や特別なDG代数の特異圏などの例が知られている. 環上の単純加群全体の持つ性質を(-d)-Calabi-Yau三角圏で公理化した概念がd単純系(d-simple-minded system)である. Jinとの共同研究で, Dynkin箙の(-d)団圏におけるd単純系の個数が, 組み合わせ論で重要な正Fuss-Catalan数で与えられることを示した.
    <BR>
    2次元の単純特異点(Du Val特異点)が有限表現型(直既約反射的加群の同型類が有限個)であることは古典的事実だが, この3次元類似をcDV特異点に対してWemyssとの共同研究で与えた. 自己準同型環がCohen-Macaulayとなるような反射的加群をmodifyingと呼ぶが, 近年, 傾理論との関連から多くの研究がなされている. cDV特異点のmodifying加群の同型類の集合から, 拡大Dynkin型の部分Tits cone内の格子点への単射を構成し, 孤立特異点ならば全単射となることを示した. 構成には拡大Dynkin型前射影多元環の傾理論が本質的に用いられる. これに関しては次年度も引き続き研究を行う.
    <BR>
    Buchweitz, Hilleとの共同研究で, 射影代数多様体上のベクトル束の圏の団傾部分圏(cluster tilting subcategory)を研究した. 例えば射影空間P^dの場合, 直線束の直和の全体がd団傾部分圏をなすが, この事実はHorrocksによる分裂判定法と等価である. より一般にd次元Fano多様体が, 傾ベクトル束Tで自己準同型環の大域次元がdとなるものを持てば, ベクトル束の圏のd団傾部分圏をTから構成できる. 証明にはd無限表現型多元環の理論が用いられる. これに関しては次年度も引き続き研究を行う.
    団圏のd単純系に関する論文が完成し, cDV特異点のmodifying加群と射影多様体の団傾理論の論文作成が大幅に前進した.
    引き続き, Auslander-Reiten理論, 傾理論, 団傾理論, 非可換特異点解消などに関する諸問題に関して, じっくりと取り組む予定である.

  4. 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.

  5. Foundations of rigid geometry from birational viewpoint

    Grant number:15H03607  2015.4 - 2019.3

    FUJIWARA KAZUHIRO

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    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.