Shimomoto Kazuma 下元数馬

… Alternative Names

SHIMOMOTO Kazuma 下元数馬

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Researcher Number	70588780
Other IDs
Affiliation (Current)	2025: 東京科学大学, 理学院, 教授
Affiliation (based on the past Project Information) *help	2023 – 2024: 東京工業大学, 理学院, 教授 2019 – 2022: 日本大学, 文理学部, 教授 2015 – 2018: 日本大学, 文理学部, 准教授 2013 – 2014: 明治大学, 理工学部, 助教 2011: 明治大学, 研究・知財戦略機構, ポスト・ドクター 2010: 明治大学, 研究・知財戦略機構, 研究員
Review Section/Research Field	Principal Investigator Basic Section 11010:Algebra-related / Algebra Except Principal Investigator Basic Section 11010:Algebra-related / Algebra
Keywords	Principal Investigator 可換環論 / 特異点 / ホモロジカル予想 / パーフェクトイド代数 / エタールコホモロジー / Frobenius写像 / 概純性定理 / Witt環 / 岩澤理論 / フロベニウス写像 … More / 局所エタールコホモロジー / パーフェクトイド化関手 / イデアル類群 / 対数的正則局所環 / 数論的可換環 / エタール射 / Tate環 / Tate環と完備化 / Riemann拡張定理 / 非完備化 / 対数的正則特異点 / パーフェクトイド・タワー / パーフェクトイド環 / ネーター環の変形問題 / Cohen-Macaulay代数 / 概可換環論 / パーフェクトイド空間 / Banach環 / 代数多様体の特異点 / 特異点論への応用 / 数論への応用 / 代数学 / 局所Bertini型定理 / Witt環の構造解析 / 特性イデアル / 肥田変形 / Bertini型定理 / フロベニウス射 / フロベウス写像 / ゼータ関数 / ベルティニ型定理 / p-進ヘッケ環 / モジュラー形式 / F-特異点 / 密着閉包 / 代数幾何への応用 / 数論 … More Except Principal Investigator Euler系 / Selmer群 / p進L関数 / 肥田理論 / 岩澤理論 / セルマー群 / オイラー系 / 岩澤朱予想 / 肥田変形 / 不分岐コホモロジー群 / 双有理不変量 / 有理性問題 / ハッセ・ノルム原理 / 代数的トーラス / Coleman変形 / Coleman写像 / p進L函数 / ジーゲルモジュラー形式 / ジーゲルモジュラー / 保型L関数 / Euler形式 / p進モジュラー形式 Less

Number theory and algebraic geometry and computer mathematics - New developments on rationality problems for algebraic varieties -
- Principal Investigator
  
  星明考
- Project Period (FY)
  2024 – 2026
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  Niigata University
変形理論、非可換化の融合による岩澤理論の新展開
- Principal Investigator
  
  落合理
- Project Period (FY)
  2023 – 2027
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  Tokyo Institute of Technology
Research on commutative rings via etale cohomology theoryPrincipal Investigator
- Principal Investigator
  
  下元数馬
- Project Period (FY)
  2023 – 2025
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  Tokyo Institute of Technology
A study on perfectoid spaces and applications to commutative ring theoryPrincipal Investigator
- Principal Investigator
  
  SHIMOMOTO Kazuma
- Project Period (FY)
  2018 – 2022
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  Nihon University
Generalization of Iwasawa theory through Galois doformation and search for new phenomena
- Principal Investigator
  
  Ochiai Tadashi
- Project Period (FY)
  2014 – 2019
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  Osaka University
Homological conjectures and applications to arithmetic geometryPrincipal Investigator
- Principal Investigator
  
  SHIMOMOTO Kazuma
- Project Period (FY)
  2013 – 2015
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Algebra
- Research Institution
  Nihon University
  Meiji University
Study on homological conjectures and their applicationsPrincipal Investigator
- Principal Investigator
  
  SHIMOMOTO Kazuma
- Project Period (FY)
  2010 – 2011
- Research Category
  
  Grant-in-Aid for Research Activity Start-up
- Research Field
  
  Algebra
- Research Institution
  Meiji University

All 2024 2023 2022 2021 2020 2019 2018 2016 2015 2014 2013 2011 2010

All Journal Article Presentation

[Journal Article] Surjectivity of some local cohomology map and the second vanishing theorem2023
- Author(s)
  Asgharzadeh Mohsen、Ishiro Shinnosuke、Shimomoto Kazuma
- Journal Title
  
  Proceedings of the American Mathematical Society
  
  Volume: 151 Issue: 7 Pages: 2847-2862
- DOI
  10.1090/proc/16340
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-23K03077
[Journal Article] Remarks on the small Cohen-Macaulay conjecture and new instances of maximal Cohen-Macaulay modules2023
- Author(s)
  Shimomoto Kazuma、Tavanfar Ehsan
- Journal Title
  
  Journal of Algebra
  
  Volume: 634 Pages: 667-697
- DOI
  10.1016/j.jalgebra.2023.06.045
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-23K03077
[Journal Article] A VARIANT OF PERFECTOID ABHYANKAR’S LEMMA AND ALMOST COHEN?MACAULAY ALGEBRAS2023
- Author(s)
  NAKAZATO KEI、SHIMOMOTO KAZUMA
- Journal Title
  
  Nagoya Mathematical Journal
  
  Volume: 253 Pages: 164-215
- DOI
  10.1017/nmj.2023.23
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-23K03077, KAKENHI-PROJECT-23K12952
[Journal Article] Finite etale extensions of Tate rings and decompletion of perfectoid algebras2022
- Author(s)
  Kei Nakazato, Kazuma Shimomoto
- Journal Title
  
  Journal of Algebra
  
  Volume: 589 Pages: 114-158
- DOI
  10.1016/j.jalgebra.2021.09.018
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K03257
[Journal Article] Weak normality and seminormality in the mixed characteristic case2022
- Author(s)
  Horiuchi Jun、Shimomoto Kazuma
- Journal Title
  
  Journal of Commutative Algebra
  
  Volume: 14 Issue: 3 Pages: 351-363
- DOI
  10.1216/jca.2022.14.351
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K03257
[Journal Article] Another proof of the almost purity theorem for perfectoid valuation rings2022
- Author(s)
  Shinnosuke Ishiro, Kazuma Shimomoto
- Journal Title
  
  Journal of Pure and Applied Algebra
  
  Volume: 226 Issue: 7 Pages: 106898-106898
- DOI
  10.1016/j.jpaa.2021.106898
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K03257
[Journal Article] Ideal-adic completion of quasi-excellent rings (after Gabber)2021
- Author(s)
  Kazuhiko Kurano, Kazuma Shimomoto
- Journal Title
  
  Kyoto J. Math.
  
  Volume: 61 Issue: 3 Pages: 707-722
- DOI
  10.1215/21562261-2021-0011
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K03226, KAKENHI-PROJECT-18K03257, KAKENHI-PROJECT-19H00637
[Journal Article] Ideal-adic completion of quasi-excellent rings (after Gabber)2020
- Author(s)
  Kurano Kazuhiko、Kazuma Shimomoto
- Journal Title
  
  Kyoto Journal of Mathematics
  
  Volume: -
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K03257
[Journal Article] A study of quasi-Gorenstein rings II: Deformation of quasi-Gorenstein property2020
- Author(s)
  Kazuma Shimomoto, Naoki Taniguchi, Ehsan Tavanfar
- Journal Title
  
  Journal of Algebra
  
  Volume: 562 Pages: 368-389
- DOI
  10.1016/j.jalgebra.2020.06.032
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03257, KAKENHI-PROJECT-20K14299
[Journal Article] Normal hyperplane sections of normal schemes in mixed characteristic2019
- Author(s)
  Jun Horiuchi, Kazuma Shimomoto
- Journal Title
  
  Communications in Algebra
  
  Volume: 印刷中
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K03257
[Journal Article] Normal hyperplane sections of normal schemes in mixed characteristic2019
- Author(s)
  Horiuchi Jun、Shimomoto Kazuma
- Journal Title
  
  Communications in Algebra
  
  Volume: 47 Issue: 6 Pages: 2412-2425
- DOI
  10.1080/00927872.2018.1470244
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K03257
[Journal Article] Integral perfectoid big Cohen-Macaulay algebras via Andre's theorem2018
- Author(s)
  Kazuma Shimomoto
- Journal Title
  
  Mathematische Annalen
  
  Volume: 372 Issue: 3-4 Pages: 1167-1188
- DOI
  10.1007/s00208-018-1704-x
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K03257
[Journal Article] An elementary proof of Cohen-Gabber theorem in the equal characteristic p>0 case2018
- Author(s)
  Kazuma Shimomoto and K. Kurano
- Journal Title
  
  Tohoku Math Journal
  
  Volume: 70 Pages: 377-389
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-26287005
[Journal Article] AN ELEMENTARY PROOF OF COHEN-GABBER THEOREM IN THE EQUAL CHARACTERISTIC $p>0$ CASE2018
- Author(s)
  Kurano Kazuhiko, Kazuma Shimomoto
- Journal Title
  
  Tohoku Mathematical Journal, Second Series
  
  Volume: 70 Issue: 3 Pages: 377-389
- DOI
  10.2748/tmj/1537495352
- ISSN
  0040-8735, 2186-585X
- Year and Date
  2018-09-30
- Language
  English
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K03257
[Journal Article] On the semicontinuity problem of fibers and global F-regularity2016
- Author(s)
  K. Shimomoto
- Journal Title
  
  Communications in Algebra
  
  Volume: 印刷中
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-25800028
[Journal Article] An application of the almost purity theorem to the homological conjectures2016
- Author(s)
  K. Shimomoto
- Journal Title
  
  Journal of Pure and Applied Algebra
  
  Volume: 220 Issue: 2 Pages: 621-632
- DOI
  10.1016/j.jpaa.2015.07.008
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-25800028
[Journal Article] Bertini theorem for normality on local rings in mixed characteristic (applications to characteristic ideals)2015
- Author(s)
  T. Ochiai and K. Shimomoto
- Journal Title
  
  Nagoya Mathematics Journal
  
  Volume: 218 Pages: 125-173
- DOI
  10.1215/00277630-2891620
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-25800028
[Journal Article] On the Witt vectors of perfect rings in positive characteristic2015
- Author(s)
  K. Shimomoto
- Journal Title
  
  Communications in Algebra
  
  Volume: 印刷中
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-25800028
[Journal Article] On the Witt vectors of perfect rings in positive characteristic2015
- Author(s)
  K. shimomoto
- Journal Title
  
  Communications in Algebra
  
  Volume: 43 Issue: 12 Pages: 5328-5342
- DOI
  10.1080/00927872.2014.974259
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-25800028
[Journal Article] Bertini theorem for normality on local rings in mixed characteristic (applications to characteristic ideals)2015
- Author(s)
  T. Ochiai, K. Shimomoto
- Journal Title
  
  Nagoya Mathematical Journal
  
  Volume: 印刷中
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-25800028
[Journal Article] Deformation of F-injectivity and local cohomology2014
- Author(s)
  J.Horiuchi, L.E.Miller, K.Shimomoto
- Journal Title
  
  Indiana University Mathematics Journal
  
  Volume: 印刷中
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-25800028
[Journal Article] Deformation of F-injectivity and local cohomology2014
- Author(s)
  J. Horiuchi, L. E. Miller, K. Shimomoto
- Journal Title
  
  Indiana University Mathematics Journal
  
  Volume: 63 Issue: 4 Pages: 1139-1157
- DOI
  10.1512/iumj.2014.63.5313
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-25800028
[Journal Article] F-coherent rings with applications to tight closure theory2011
- Author(s)
  下元数馬
- Journal Title
  
  Journal of Algebra
  
  Volume: 338巻 Issue: 1 Pages: 24-34
- DOI
  10.1016/j.jalgebra.2011.05.006
- ISSN
  0021-8693
- Data Source
  KAKENHI-PROJECT-22840042
[Presentation] パーフェクトイド空間とネーター環論への応用2024
- Author(s)
  下元数馬
- Organizer
  2024早稲田整数論研究集会
- Invited
- Data Source
  KAKENHI-PROJECT-23K03077
[Presentation] Singularities in arithmetic geometry2023
- Author(s)
  下元数馬
- Organizer
  代数的整数論とその周辺2023
- Invited
- Data Source
  KAKENHI-PROJECT-23K03077
[Presentation] On p-adic deformation of cohomology theory and singularities2023
- Author(s)
  下元数馬
- Organizer
  第44回可換環論シンポジウム
- Data Source
  KAKENHI-PROJECT-23K03077
[Presentation] Almost Cohen-Macaulay algebras2022
- Author(s)
  下元数馬
- Organizer
  Virtual commutative algebra seminar in Tehran
- Invited
- Data Source
  KAKENHI-PROJECT-18K03257
[Presentation] Perfectoid Spaces-Part 12021
- Author(s)
  下元数馬
- Organizer
  Virtual Commutative Algebra Seminars
- Invited
- Data Source
  KAKENHI-PROJECT-18K03257
[Presentation] 変形理論によるネーター環の探索2021
- Author(s)
  下元数馬
- Organizer
  第42回可換環論シンポジウム
- Data Source
  KAKENHI-PROJECT-18K03257
[Presentation] 数論と可換環論の応用ーホモロジカル予想を超えてー2021
- Author(s)
  下元数馬
- Organizer
  日本数学会・秋季総合分科会
- Invited
- Data Source
  KAKENHI-PROJECT-18K03257
[Presentation] Perfectoid Spaces-Part 22021
- Author(s)
  下元数馬
- Organizer
  Virtual Commutative Algebra Seminars
- Invited
- Data Source
  KAKENHI-PROJECT-18K03257
[Presentation] Almost integrality and almost finite etale extensions (joint with Kei Nakazato)2019
- Author(s)
  Kei Nakazato、Kazuma Shimomoto
- Organizer
  第41回可換環シンポジウム
- Data Source
  KAKENHI-PROJECT-18K03257
[Presentation] Decompleting perfectoid algebras and the almost purity theorem2019
- Author(s)
  Kazuma Shimomoto
- Organizer
  Morgantown Algebra Days
- Invited
- Data Source
  KAKENHI-PROJECT-18K03257
[Presentation] What is perfectoid commutative ring theory?2019
- Author(s)
  下元数馬
- Organizer
  West Virgina University, Algebra Seminar/Colloquium
- Invited
- Data Source
  KAKENHI-PROJECT-18K03257
[Presentation] Decompleting perfectoid Abhyankar's lemma and almost Cohen-Macaulay algebras (joint with Kei Nakazato)2019
- Author(s)
  Kazuma Shimomoto、Kei Nakazato
- Organizer
  第41回可換環シンポジウム
- Data Source
  KAKENHI-PROJECT-18K03257
[Presentation] 疑ゴレンシュタイン環の変形問題2018
- Author(s)
  下元数馬
- Organizer
  東大可換環論セミナー
- Data Source
  KAKENHI-PROJECT-18K03257
[Presentation] F-singularities and non Cohen-Macaulay rings2016
- Author(s)
  下元数馬
- Organizer
  Commutative Algebra Seminar
- Place of Presentation
  ユタ大学
- Year and Date
  2016-03-11
- Data Source
  KAKENHI-PROJECT-25800028
[Presentation] Cohen-Gabberの定理の初等的な証明について2015
- Author(s)
  下元数馬
- Organizer
  代数セミナー
- Place of Presentation
  中央大学
- Year and Date
  2015-11-27
- Invited
- Data Source
  KAKENHI-PROJECT-25800028
[Presentation] A new proof of a theorem of Cohen and Gabber2015
- Author(s)
  下元数馬
- Organizer
  Commutative Algebra Seminar
- Place of Presentation
  ユタ大学
- Year and Date
  2015-09-11
- Data Source
  KAKENHI-PROJECT-25800028
[Presentation] An application of a theorem of Cohen and Gabber to Bertini-type theorem on local rings of positive characteristic2015
- Author(s)
  下元数馬
- Organizer
  The JV Seminar on Commutative Algebra
- Place of Presentation
  明治大学
- Year and Date
  2015-09-19
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-25800028
[Presentation] A new proof of a theorem of Cohen and Gabber2015
- Author(s)
  下元数馬
- Organizer
  可換環論シンポジウム37回
- Place of Presentation
  岡山県倉敷市
- Year and Date
  2015-11-22
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-25800028
[Presentation] On the structure of the Witt-Frobenius map2014
- Author(s)
  K. Shimomoto
- Organizer
  第36回可換環論シンポジウム
- Place of Presentation
  神奈川県、葉山
- Year and Date
  2014-11-22
- Invited
- Data Source
  KAKENHI-PROJECT-25800028
[Presentation] Almost purity theorem and big Cohen-Macaulay algebras in mixed characteristic2013
- Author(s)
  下元数馬
- Organizer
  Birational geometry and Singularities in Positive characteristic
- Place of Presentation
  東京大学大学院数理科学科研究科
- Invited
- Data Source
  KAKENHI-PROJECT-25800028
[Presentation] Almost purity and the homological conjectures2013
- Author(s)
  下元数馬
- Organizer
  可換環論シンポジウム35回
- Place of Presentation
  京都大学数理解析研究所
- Data Source
  KAKENHI-PROJECT-25800028
[Presentation] Almost purity and the homological conjectures2013
- Author(s)
  下元数馬
- Organizer
  イリノイ大学代数学セミナー
- Place of Presentation
  イリノイ大学、米国
- Invited
- Data Source
  KAKENHI-PROJECT-25800028
[Presentation] Galois cohomology and Selmer group over normal domains2011
- Author(s)
  下元数馬
- Organizer
  The 7-th Japan-Vietnam Seminar
- Place of Presentation
  ベトナム・クイニョン大学
- Year and Date
  2011-12-13
- Data Source
  KAKENHI-PROJECT-22840042
[Presentation] 局所ベルティニ定理と岩澤予想への応用2010
- Author(s)
  下元数馬
- Organizer
  第32回可換環論シンポジウム
- Place of Presentation
  神奈川県三浦郡葉山町湘南国際村
- Year and Date
  2010-12-12
- Data Source
  KAKENHI-PROJECT-22840042

1. Ochiai Tadashi (90372606)

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2. 原隆 (40722608)

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3. 安田正大 (90346065)

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4. 星明考 (50434262)

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5. 山崎愛一 (10283590)

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6. 木田雅成 (20272057)

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13. 蔵野和彦

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Shimomoto Kazuma 下元 数馬

SHIMOMOTO Kazuma 下元 数馬

Research Projects

Research Products

Co-Researchers

Number theory and algebraic geometry and computer mathematics - New developments on rationality problems for algebraic varieties -

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

変形理論、非可換化の融合による岩澤理論の新展開

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Research on commutative rings via etale cohomology theoryPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

A study on perfectoid spaces and applications to commutative ring theoryPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Generalization of Iwasawa theory through Galois doformation and search for new phenomena

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Homological conjectures and applications to arithmetic geometryPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Study on homological conjectures and their applicationsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

[Journal Article] Surjectivity of some local cohomology map and the second vanishing theorem2023

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Remarks on the small Cohen-Macaulay conjecture and new instances of maximal Cohen-Macaulay modules2023

Author(s)

Journal Title

DOI

Data Source

[Journal Article] A VARIANT OF PERFECTOID ABHYANKAR’S LEMMA AND ALMOST COHEN?MACAULAY ALGEBRAS2023

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Finite etale extensions of Tate rings and decompletion of perfectoid algebras2022

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Weak normality and seminormality in the mixed characteristic case2022

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Another proof of the almost purity theorem for perfectoid valuation rings2022

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Ideal-adic completion of quasi-excellent rings (after Gabber)2021

Author(s)

Journal Title

Shimomoto Kazuma 下元数馬

SHIMOMOTO Kazuma 下元数馬

[Journal Article] AN ELEMENTARY PROOF OF COHEN-GABBER THEOREM IN THE EQUAL CHARACTERISTIC $p>0$ CASE2018