Updated on 2024/10/28
博士（数理科学） （ 2012.3 東京大学 ）
修士（数理科学） （ 2009.3 東京大学 ）
学士（理学） （ 2007.3 東京大学 ）
Natural Science / Algebra / 整数論、p進微分方程式
p進微分方程式の解の対数的増大度
非アルキメデス完備体上の微分加群の理論
Japan Society for Promotion of Science
2010.4 - 2012.3
Country：Japan
The University of Tokyo
2009.4 - 2012.3
Country： Japan
The University of Tokyo
2007.4 - 2009.3
Country： Japan
The University of Tokyo
2003.4 - 2007.3
Country： Japan
日本数学会
日本数学会賞建部賢弘賞奨励賞
2014.9 日本数学会
Duality for differential modules over complete non-archimedean valuation fields of characteristic zero
Shun Ohkubo
arXiv:2404.16291 2024.4
Logarithmic growth filtrations for (φ,∇)-modules over the bounded Robba ring Reviewed
Shun Ohkubo
Compositio Mathematica Vol. 157 ( 6 ) page： 1265 - 1301 2021.6
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
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
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
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
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
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
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
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
A note on Sen's theory in the imperfect residue field case Reviewed
Shun Ohkubo
Mathematische Zeitschrift Vol. 269 page： 261 - 280 2010.5
Duality for differential modules over complete non-archimedean valuation field of characteristic zero Invited International conference
Shun Ohkubo
$p$-adic cohomology and arithmetic geometry--A conference on the occasion of Nobuo Tsuzuki's 60th birthday-- 2024.10.22
A note on the variation of subsidiary radii of $p$-adic differential equations in the regular singular case Invited International conference
Shun Ohkubo
Around $p$-adic cohomologies 2022.9.21
Shun Ohkubo
2024.5.28
Around $p$-adic cohomologies, $L$-functions and Motives in Niseko 2022 2022.9.10
2021.2.22
Logarithmic growth f.iltrations for (φ, ∇)-modules over the bounded Robba ring
Algebraic Number Theory and Related Topics 2019
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
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
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
On differential modules associated to de Rham representations in the imperfect residue field case
Shun Ohkubo
Seminaire de Geometrie Arithmetique Paris-Pekin-Tokyo
On differential modules associated to de Rham representations in the imperfect residue field case International conference
Shun Ohkubo
Workshop on Algebraic Number Theory
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
On differential modules associated to de Rham representations in the imperfect residue field case International conference
Shun Ohkubo
Symposium on Arithmetic Geometry
The p-adic monodromy theorem in the imperfect residue field case
On a horizontal analogue of the p-adic monodromy theorem
A note on Sen's theory in the imperfect residue field case
A note on Sen's theory in the imperfect residue field case
A note on Sen's theory in the imperfect residue field case
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
A new development of arithmetic geometry by p-adic methods
Grant number：24H00015 2024.4 - 2029.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (S)
Authorship：Coinvestigator(s)
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
日本学術振興会 科学研究費補助金 基盤研究(C)
Authorship：Principal investigator Grant type：Competitive
Grant amount：\4160000 （ Direct Cost: \3200000 、 Indirect Cost：\960000 ）
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
日本学術振興会 科学研究費補助金 若手研究(B)
Authorship：Principal investigator Grant type：Competitive
Grant amount：\4160000 （ Direct Cost: \3200000 、 Indirect Cost：\960000 ）
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
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。
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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。
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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。
Foundations of rigid geometry from birational viewpoint
Grant number：15H03607 2015.4 - 2019.3
FUJIWARA KAZUHIRO
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.
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
Authorship：Principal investigator Grant type：Competitive
Grant amount：\3630000 （ Direct Cost: \3300000 、 Indirect Cost：\330000 ）
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
Authorship：Principal investigator Grant type：Competitive
Grant amount：\1400000 （ Direct Cost: \1400000 ）
Exercise in Mathematics IV
2023
Exercise in Mathematics III
2023
Undergraduate Seminar ZI
2023
Undergraduate Seminar ZII
2023
Exercise in Mathematics VIII
2022
Exercise in Mathematics VII
2022
Exercise in Mathematics VII
2021
Undergraduate Seminar DI
2021
Exercise in Mathematics VIII
2021
Undergraduate Seminar DII
2021
Exercise in Mathematics II
2020
数学演習II
2020
数学演習II
2019
数学演習V・VI
2018
数学演習I
2017
数学演習VII・VIII
2016
数学演習VII・VIII
2015
楕円曲線の整数論
Role(s)：Lecturer
数学アゴラ 2016.8
楕円曲線の整数論その2
Role(s)：Lecturer
ＮＨＫ文化センター名古屋 数学散策 2018.3
楕円曲線の整数論
Role(s)：Lecturer
ＮＨＫ文化センター名古屋 数学散策 2017.4
