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Study on homological conjectures and their applications

Research Project

Project/Area Number 22840042
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionMeiji University

Principal Investigator

SHIMOMOTO Kazuma  明治大学, 研究・知財戦略機構, ポスト・ドクター (70588780)

Project Period (FY) 2010 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥1,846,000 (Direct Cost: ¥1,420,000、Indirect Cost: ¥426,000)
Fiscal Year 2011: ¥1,001,000 (Direct Cost: ¥770,000、Indirect Cost: ¥231,000)
Fiscal Year 2010: ¥845,000 (Direct Cost: ¥650,000、Indirect Cost: ¥195,000)
Keywords数論 / 代数幾何への応用 / フロベニウス写像 / 密着閉包 / F-特異点 / ホモロジカル予想 / 岩澤理論 / モジュラー形式 / p-進ヘッケ環 / ベルティニ型定理 / 可換環論 / 特異点 / ゼータ関数 / フロベウス写像
Research Abstract

I made an extensive study on homological conjectures in commutative algebra and developed some algebraic techniques. These techniques were applied to consider applications to singularities arising from algebraic geometry and the main conjecture of Iwasawa theory on modular forms.

Report

(3 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • Research Products

    (6 results)

All 2011 2010

All Journal Article (1 results) Presentation (5 results)

  • [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
    • Related Report
      2011 Annual Research Report 2011 Final Research Report 2010 Annual Research Report
  • [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
    • Related Report
      2011 Annual Research Report
  • [Presentation] Local Bertini theorem and the Iwasawa main conjecture2011

    • Place of Presentation
      ユタ大学
    • Year and Date
      2011-02-26
    • Related Report
      2011 Final Research Report
  • [Presentation] Workshop on almost purity at Ann Arbor2011

    • Place of Presentation
      ミシガン大学
    • Related Report
      2011 Final Research Report
  • [Presentation]2011

    • Organizer
      The 7-th Japan-Vietnam Seminar
    • Place of Presentation
      クイニョン大学(ベトナム)
    • Related Report
      2011 Final Research Report
  • [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
    • Related Report
      2010 Annual Research Report

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Published: 2010-08-27   Modified: 2016-04-21  

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