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Studies on canonical and n-canonical modules

Research Project

Project/Area Number 17K05203
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionOsaka City University (2019-2020)
Okayama University (2017-2018)

Principal Investigator

Hashimoto Mitsuyasu  大阪市立大学, 大学院理学研究科, 教授 (10208465)

Project Period (FY) 2017-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords標準加群 / n 標準加群 / ヤコビアン予想 / Zariski-Nagata の定理 / n標準加群 / エタール射 / 次数付き加群 / 同型 / 直既約性 / 不分岐射 / purity / 擬有限 / Serre の条件 / Purity / ネーター環 / 正準加群 / quasi-Gorenstein / ねじれ逆像
Outline of Final Research Achievements

We studied on canonical and n-canonical modules. We have suceeded in removing the extra hypothesis of the quasi-finiteness under mild conditions that the schemes in problem are over some fields. In the proof of the theorem, we have used D-modules and their relatives. The theorem is expected to be applicable to the study of Jacobian Conjecture which asserts that an etale endomorphism of an affine n-space over a field of characteristic zero is an isomorphism. Moreover, the study on canonical modules will be applicable to the study on almost Gorenstein property, which lies between the Cohen-Macaulay property and the Gorenstein property.

Academic Significance and Societal Importance of the Research Achievements

標準加群やその類似物の研究は可換環論・代数幾何学の進歩のために必要である。ヤコビアン予想はアメリカ数学会の分類表においてもひとつのテーマとして掲げられるほどに重要なアフィン代数幾何学上の懸案であり、その解決は待ち望まれており、学術的意義は高い。この問題の解決に資すると思われることが今回証明できた。純粋数学の問題であり、直接の社会的意義は無い。

Report

(5 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (8 results)

All 2019 2018 2017 2016

All Journal Article (5 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 5 results,  Acknowledgement Compliant: 3 results) Presentation (3 results) (of which Int'l Joint Research: 1 results,  Invited: 1 results)

  • [Journal Article] F-rationality of the ring of modular invariants2017

    • Author(s)
      Mitsuyasu Hashimoto
    • Journal Title

      Journal of Algebra

      Volume: 484 Pages: 207-223

    • DOI

      10.1016/j.jalgebra.2017.04.017

    • NAID

      120006712858

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] The asymptotic behavior of Frobenius direct images of rings of invariants2017

    • Author(s)
      Mitsuyasu Hashimoto and Peter Symonds
    • Journal Title

      Advances in Mathematics

      Volume: 305 Pages: 144-164

    • DOI

      10.1016/j.aim.2016.09.020

    • NAID

      120006547366

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Equivariant class group II. Enriched descent theorem2017

    • Author(s)
      Mitsuyasu Hashimoto
    • Journal Title

      Communications in Algebra

      Volume: 45 Issue: 4 Pages: 1509-1532

    • DOI

      10.1080/00927872.2016.1178270

    • NAID

      120006352348

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Higher-dimensional absolute versions of symmetric, Frobenius, and quasi-Frobenius algebras2017

    • Author(s)
      Mitsuyasu Hashimoto
    • Journal Title

      Math. J. Okayama Univ.

      Volume: 59 Pages: 131-140

    • NAID

      120005898813

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Canonical and n-canonical modules of a Noetherian algebra2016

    • Author(s)
      Mitsuyasu Hashimoto
    • Journal Title

      Nagoya Mathematical Journal

      Volume: on line Pages: 1-39

    • DOI

      10.1017/nmj.2016.44

    • NAID

      120006366608

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Zariski-Nagata の定理について2019

    • Author(s)
      橋本光靖
    • Organizer
      東京可換環論セミナー
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Zariski-Nagata の定理の改良について2018

    • Author(s)
      橋本光靖
    • Organizer
      Commutative Algebra Day in Kyoto
    • Related Report
      2018 Research-status Report
  • [Presentation] F-rationality of invariant subrings2017

    • Author(s)
      Mitsuyasu Hashimoto
    • Organizer
      PRIMA 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research

URL: 

Published: 2017-04-28   Modified: 2022-01-27  

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