仿射delign - lusztig品种混合特性的等维性

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-02-14 DOI:10.1016/j.aim.2025.110153

Yuta Takaya

{"title":"仿射delign - lusztig品种混合特性的等维性","authors":"Yuta Takaya","doi":"10.1016/j.aim.2025.110153","DOIUrl":null,"url":null,"abstract":"<div><div>We prove the equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic. This verifies a conjecture made by Rapoport and implies that the results of Nie and Zhou-Zhu can be extended to the whole irreducible components of affine Deligne-Lusztig varieties. The method is to translate the work of Hartl-Viehmann into mixed characteristic and construct local foliations for affine Deligne-Lusztig varieties. This leads us to develop a theory of formal algebraic geometry for perfect schemes.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"465 ","pages":"Article 110153"},"PeriodicalIF":1.5000,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic\",\"authors\":\"Yuta Takaya\",\"doi\":\"10.1016/j.aim.2025.110153\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We prove the equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic. This verifies a conjecture made by Rapoport and implies that the results of Nie and Zhou-Zhu can be extended to the whole irreducible components of affine Deligne-Lusztig varieties. The method is to translate the work of Hartl-Viehmann into mixed characteristic and construct local foliations for affine Deligne-Lusztig varieties. This leads us to develop a theory of formal algebraic geometry for perfect schemes.</div></div>\",\"PeriodicalId\":50860,\"journal\":{\"name\":\"Advances in Mathematics\",\"volume\":\"465 \",\"pages\":\"Article 110153\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2025-02-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0001870825000519\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0001870825000519","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们证明了仿射delign - lusztig变体在混合特征中的等维性。这证实了Rapoport的一个猜想，并暗示了Nie和Zhou-Zhu的结果可以推广到仿射delign - lusztig变种的整个不可约分量。该方法是将Hartl-Viehmann的工作转化为混合特征，并构造仿射delign - lusztig品种的局部叶。这引导我们为完美方案发展一种形式代数几何理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic

We prove the equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic. This verifies a conjecture made by Rapoport and implies that the results of Nie and Zhou-Zhu can be extended to the whole irreducible components of affine Deligne-Lusztig varieties. The method is to translate the work of Hartl-Viehmann into mixed characteristic and construct local foliations for affine Deligne-Lusztig varieties. This leads us to develop a theory of formal algebraic geometry for perfect schemes.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.