Noncommutative resolution of singularities in positive characteristic and its applications

正特征奇点的非交换消解及其应用

• 批准号: 22740020
• 负责人: YASUDA Takehiko
• 金额: $ 2.75万
• 依托单位: Osaka University (2012-2013)Kagoshima University (2010-2011)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22740020/
• 关键词: 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

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.

在与 Nobuo Hara 和 Tadakazu Sawada 的合作中，我详细研究了有理双点和简单椭圆奇点的 F 爆炸。作为非交换决议的 Frobenius 函子研究的副产品，我证明了对于余维一上自由的狂野有限群作用，相关的商奇点不是强 F 正则的。粗略地说，这意味着在温和的条件下，野商奇点总是不好的。我还开始研究通过使用动机整合将麦凯对应关系推广到积极特征。事实证明，奇点和数论密切相关。

项目成果

Stringy invariants of p-cyclic quotient singularities

p 循环商奇点的弦不变量

• 发表时间: 2013
• 作者: Wee Teck Gan;Atsushi Ichino;Takehiko Yasuda
• 通讯作者: Takehiko Yasuda

Introduction to F-blowups

F-爆炸简介

• 发表时间: 2010
• 作者: Xiao-Yu Zhang;Qing Fang;赤間陽二;古澤仁;Kimihiko Motegi;Yohji Akama;Kimihiko Motegi;Qing Fang;Hitoshi Furusawa;赤間陽二;茂手木公彦;古澤仁;Qing Fang;赤間陽二;Yohji Akama;Takehiko Yasuda
• 通讯作者: Takehiko Yasuda

Motivic integration and wild ramification

动机整合和疯狂分支

• 发表时间: 2013
• 作者: Shigeo Koshitani;Naoko Kunugi;Takehiko Yasuda
• 通讯作者: Takehiko Yasuda

Higher Nash blowups and F-blowups

更高的纳什爆炸和 F 爆炸

• 发表时间: 2012
• 作者: Y.Tachiya;T.Tanaka;T.Kurosawa;星裕一郎;Takehiko Yasuda;松野 一夫;T. Tanaka;Atsushi Ichino;星裕一郎;Takehiko Yasuda;松野一夫;Takehiko Yasuda;星裕一郎;Atsushi Ichino;T. Tanaka;松野 一夫;星裕一郎;Takehiko Yasuda;Atsushi Ichino;Taka-aki Tanaka;松野一夫;星裕一郎;T. Tanaka;松野 一夫;Atsushi Ichino;Atsushi Ichino;星裕一郎;Takehiko Yasuda;T. Tanaka;星裕一郎;Takehiko Yasuda;Takehiko Yasuda
• 通讯作者: Takehiko Yasuda

An invitation to the wild McKay correspondence

野性麦凯信件的邀请

• 发表时间: 2013
• 作者: Kaoru Hiraga;Atsushi Ichino;功刀直子;杉山和成;Yuichiro Hoshi;Naoko Kunugi;Takehiko Yasuda
• 通讯作者: Takehiko Yasuda