Updated on 2022/05/23

写真a

 
OHKUBO Shun
 
Organization
Graduate School of Mathematics Division of Mathematics Natural Mathematics Lecturer
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science Department of Mathematics
Title
Lecturer

Degree 1

  1. 博士(数理科学) ( 2012.3   東京大学 ) 

Research History 1

  1. Japan Society for Promotion of Science

    2010.4 - 2012.3

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    Country:Japan

Professional Memberships 1

  1. 日本数学会

Awards 1

  1. 日本数学会賞建部賢弘賞奨励賞

    2014.9   日本数学会  

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    Country:Japan

 

Papers 10

  1. Logarithmic growth filtrations for (φ,∇)-modules over the bounded Robba ring Reviewed

    Shun Ohkubo

    Compositio Mathematica   Vol. 157 ( 6 ) page: 1265 - 1301   2021.6

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

  2. On differential modules associated to de Rham representations in the imperfect residue field case Reviewed

    Shun Ohkubo

    Algebra and Number Theory   Vol. 9 ( 8 ) page: 1881-1954   2015.10

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

    DOI: 10.2140/ant.2015.9.1881

  3. The p-adic monodromy theorem in the imperfect residue field case Reviewed

    Shun Ohkubo

    Algebra and Number Theory   Vol. 7 ( 8 ) page: 1977 - 2037   2013.11

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

  4. Logarithmic growth filtrations for (phi, del)-modules over the bounded Robba ring Reviewed

    Ohkubo Shun

    COMPOSITIO MATHEMATICA   Vol. 157 ( 6 ) page: 1265 - 1301   2021.6

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

    DOI: 10.1112/S0010437X21007107

    Web of Science

  5. A note on logarithmic growth of solutions of p-adic differential equations without solvability Reviewed

    Ohkubo Shun

    MATHEMATICAL RESEARCH LETTERS   Vol. 26 ( 5 ) page: 1527 - 1557   2019

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

    Web of Science

  6. On the rationality and continuity of logarithmic growth filtration of solutions of p-adic differential equations Reviewed

    Shun Ohkubo

    Advances in Mathematics   Vol. 308   page: 83 - 120   2017.2

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

    DOI: 10.1016/j.aim.2016.12.006

    Web of Science

  7. On Lie algebras arising from p-adic representations in the imperfect residue field case Reviewed

    Shun Ohkubo

    Journal of Algebra   Vol. 406   page: 134 - 142   2014.5

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

  8. A note on logarithmic growth Newton polygons of p-adic differential equations Reviewed

    Shun Ohkubo

    International Mathematics Research Notices   Vol. 2015 ( 10 ) page: 2671 - 2677   2014.2

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

    DOI: 10.1093/imrn/rnu017

  9. Galois Theory of B+dR in the imperfect residue field case Reviewed

    Shun Ohkubo

    Journal of Number Theory   Vol. 130   page: 1609-1641   2010.7

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

  10. A note on Sen's theory in the imperfect residue field case Reviewed

    Shun Ohkubo

    Mathematische Zeitschrift   Vol. 269   page: 261 - 280   2010.5

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

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Presentations 15

  1. Logarithmic growth f.iltrations for (φ, ∇)-modules over the bounded Robba ring

    Algebraic Number Theory and Related Topics 2019 

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    Event date: 2019.12

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  2. A note on the convergence Newton polygons of p-adic differential equations in the regular singular case Invited

    2021.2.22 

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    Event date: 2021.2

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  3. On the rationality of the logarithmic growth filtration of solutions of p-adic differential equations Invited International conference

    Shun Ohkubo

    Geometrie analytique et equations differentielles p-adiques 

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    Event date: 2017.3

    Language:English   Presentation type:Oral presentation (general)  

    Country:France  

  4. On the rationality of the logarithmic growth filtration of solutions of p-adic differential equations International conference

    Shun Ohkubo

    Princeton University/IAS Number Theory Seminar 

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    Event date: 2015.2

    Language:English   Presentation type:Oral presentation (general)  

    Country:United States  

  5. On differential modules associated to de Rham representations in the imperfect residue field case International conference

    Shun Ohkubo

    Korea-Japan Joint Seminar on Number Theory and Related Topics 

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    Event date: 2013.1

    Language:English   Presentation type:Oral presentation (general)  

    Country:Korea, Republic of  

  6. On differential modules associated to de Rham representations in the imperfect residue field case

    Shun Ohkubo

    Seminaire de Geometrie Arithmetique Paris-Pekin-Tokyo 

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    Event date: 2013.1

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  7. On differential modules associated to de Rham representations in the imperfect residue field case International conference

    Shun Ohkubo

    Workshop on Algebraic Number Theory 

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    Event date: 2012.12

    Language:English   Presentation type:Oral presentation (general)  

    Country:New Zealand  

  8. On differential modules associated to de Rham representations in the imperfect residue field case

    Shun Ohkubo

    p-adic cohomology and its applications to arithmetic geometry 

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    Event date: 2012.10 - 2012.11

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  9. On differential modules associated to de Rham representations in the imperfect residue field case International conference

    Shun Ohkubo

    Symposium on Arithmetic Geometry 

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    Event date: 2012.10

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  10. The p-adic monodromy theorem in the imperfect residue field case

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    Event date: 2011.11 - 2011.12

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  11. On a horizontal analogue of the p-adic monodromy theorem

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    Event date: 2011.7

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  12. A note on Sen's theory in the imperfect residue field case

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    Event date: 2009.12

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  13. A note on Sen's theory in the imperfect residue field case

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    Event date: 2009.10

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  14. A note on Sen's theory in the imperfect residue field case

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    Event date: 2009.7

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  15. 剰余体が完全でない場合のB+dRのガロア理論 International conference

    大久保 俊

    代数学コロキウム 

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    Event date: 2009.5

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:東京大学   Country:Japan  

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

  1. p進解析空間上のp進微分方程式の研究

    Grant number:17K14161  2017.4 - 2022.3

    科学研究費補助金  若手研究(B)

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\4160000 ( Direct Cost: \3200000 、 Indirect Cost:\960000 )

  2. p進Hodge理論の高次元化

    Grant number:12J09128  2012.4 - 2015.3

    科学研究費補助金 

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\3630000 ( Direct Cost: \3300000 、 Indirect Cost:\330000 )

  3. p進表現とp進微分方程式の分岐理論

    Grant number:10J06817  2010.4 - 2011.3

    科学研究費補助金 

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\1400000 ( Direct Cost: \1400000 )

  4. p進微分方程式の解の対数的増大度を駆使した数論幾何学における新手法

    Grant number:22K03227  2022.4 - 2027.3

    科学研究費助成事業  基盤研究(C)

    大久保 俊

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    Authorship:Principal investigator 

    Grant amount:\4160000 ( Direct Cost: \3200000 、 Indirect Cost:\960000 )

  5. p進解析空間上のp進微分方程式の研究

    Grant number:17K14161  2017.4 - 2022.3

    科学研究費助成事業  若手研究(B)

    大久保 俊

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    Authorship:Principal investigator 

    Grant amount:\4160000 ( Direct Cost: \3200000 、 Indirect Cost:\960000 )

    1:2018年度に執筆したChiarellotto-Tsuzuki予想のpreprintを改訂し、Compositio Mathematicaに受理された。
    <BR>
    2:2019年度に引き続き、Chiarellotto-Tsuzuki予想の、$p$-adic local monodromy theoremと両立する一般化の証明に関するプレプリントの執筆を継続した。
    <BR>
    3:Spectral convergence Newton polygonの基本性質は、Kedlayaによるp-adic Differential Equations (2010)により示されている。これを、log版(つまりregular singularな場合)に拡張し、さらにBerkovich曲線上の微分方程式のconvergence Newton polygonへの応用を与えた。これらの結果をまとめたプレプリントを執筆中である。
    結果はえられている一方、論文執筆を完了する時間が十分なかった。
    研究実績の概要2、3でえられた結果をプレプリントにまとめ、さらなる応用を探る予定である。より具体的に述べると以下の通りである。Picard-Fuchs moduleはregular singularなので、概要3で述べたlog版の結果は、Picard-Fuchs moduleに適用できると期待される。そこで、P^1上の具体的な多様体の族に付随するPicard-Fuchsのconvergence Newton polygonを考察する予定である。

  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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