Homological conjectures and applications to arithmetic geometry
| Project/Area Number |
25800028
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Nihon University (2015)
Meiji University (2013-2014) |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 可換環論 / 岩澤理論 / 特異点 / ホモロジカル予想 / フロベニウス射 / Witt環 / 概純性定理 / Bertini型定理 / 肥田変形 / 特性イデアル / Witt環の構造解析 / 局所Bertini型定理 / Frobenius写像 / 代数学 / 数論への応用 / 特異点論への応用 |
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| Outline of Final Research Achievements |
I made effective use of the techniques and ideas from commutative ring and p-adic Hodge theory to study the Direct Summand Conjecture and the big Cohen-Macaulay algebras. I obtained some interesting results. While studying these questions, I also studied the ring-theoretic structure of the Witt vectors and Noetherian rings with mixed characteristic. I published a joint paper on the local Bertini theorem for normality on local rings with mixed characteristic, including its application to the characteristic ideals of certain modules, which play an important role in Iwasawa theory. Finally, let me report on a joint work on giving a partial answer to the deformation problem on a certain class of F-singularities defined by the local cohomology modules.
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Report
(4 results)
Research Products
(19 results)
