Studies on canonical and n-canonical modules

2020 Fiscal Year Final Research Report

• Project/Area Number: 17K05203
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Osaka 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
• Keywords: 標準加群 / n 標準加群 / ヤコビアン予想 / Zariski-Nagata の定理

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.

Free Research Field

代数学

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。