2013 Fiscal Year Final Research Report
Noncommutative resolution of singularities in positive characteristic and its applications
| Project/Area Number |
22740020
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Osaka University (2012-2013)
Kagoshima University (2010-2011) |
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Principal Investigator |
YASUDA Takehiko 大阪大学, 理学(系)研究科(研究院), 准教授 (30507166)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 特異点 / 特異点解消 / 非可換代数幾何 / 正標数 / モチーフ積分 / 野生商特異点 |
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| Research Abstract |
In a joint work with Nobuo Hara and Tadakazu Sawada, I studied F-blowups of rational double points and simple elliptic singularities in detail. As a byproduct of studies of Frobenius functors of noncommutative resolutions, I proved that concerning a wild finite group action which is free in codimension one, the associated quotient singularity is not strongly F-regular. Roughly, this means that under a mild condition, wild quotient singularities are always bad. Also I started a research on a generalization of the McKay correspondence to positive characteristics by using motivic integration. It has turned out that singularities and the number theory are closely related.
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