2023 Fiscal Year Final Research Report
Study of the Jacobian conjecture analyzing various families of etale morphisms between affine spaces
| Project/Area Number |
20K03538
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Osaka Metropolitan University (2022-2023)
Osaka City University (2020-2021) |
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Principal Investigator |
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Keywords | エタール射 / 可換環論 / 多項式環 |
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| Outline of Final Research Achievements |
The study was to solve the Jacobian Conjecture, which is an important problem in commutative algebra and algebraic geometry from the viewpoint of commutative algebra in positive characteristic. Given a tame etale endomorphism of affine spaces, we consider a polynomial ring with a new variable, and discussed the ring theoretic properties of its subrings.
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| Free Research Field |
可換環論
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| Academic Significance and Societal Importance of the Research Achievements |
ヤコビアン予想はアメリカ数学会の Mathematics Subject Classification において、独自の分類番号を持っているくらいに重要性の高い代数幾何学および可換環論における未解決問題であり、解決できた場合のインパクトは計り知れない。今回の研究において、正標数の可換環論を用いたアプローチにより、この問題を解決するのに何が分かれば良いかが分かったといえる。
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