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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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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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 / 野生McKay対応 / 点のHilbertスキーム / Bhargavaの量公式 / 局所Galois表現 / Deligne-Mumfordスタック / マッカイ対応 / 野生的商特異点 / 悲観特異点解消 / F爆発 / フロベニウス射 / 非可換特異点解消 |
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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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Report
(5 results)
Research Products
(47 results)
