De Rham F $F$ -gauges and Shimura varieties

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-29 DOI:10.1112/jlms.70309

Xu Shen

{"title":"De Rham \n \n F\n $F$\n -gauges and Shimura varieties","authors":"Xu Shen","doi":"10.1112/jlms.70309","DOIUrl":null,"url":null,"abstract":"We study <math>\n <semantics>\n <mi>F</mi>\n <annotation>$F$</annotation>\n </semantics></math>-gauges for de Rham cohomology of smooth algebraic varieties in characteristic <math>\n <semantics>\n <mi>p</mi>\n <annotation>$p$</annotation>\n </semantics></math>. Applying to good reductions of Shimura varieties of Hodge type, we recover the Ekedahl–Oort stratifications by constructing universal de Rham <math>\n <semantics>\n <mi>F</mi>\n <annotation>$F$</annotation>\n </semantics></math>-gauges with <math>\n <semantics>\n <mi>G</mi>\n <annotation>$G$</annotation>\n </semantics></math>-structure. We also study the cohomology of de Rham <math>\n <semantics>\n <mi>F</mi>\n <annotation>$F$</annotation>\n </semantics></math>-gauges on these varieties. In particular, in the PEL-type case and when the weights of the flat automorphic vector bundles are <math>\n <semantics>\n <mi>p</mi>\n <annotation>$p$</annotation>\n </semantics></math>-small, we determine the <math>\n <semantics>\n <mi>F</mi>\n <annotation>$F$</annotation>\n </semantics></math>-gauge structure on their de Rham cohomology by the associated dual Bernstein-Gelfand-Gelfand (BGG) complexes.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 4","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70309","RegionNum":2,"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

Abstract

We study $F$ -gauges for de Rham cohomology of smooth algebraic varieties in characteristic $p$ . Applying to good reductions of Shimura varieties of Hodge type, we recover the Ekedahl–Oort stratifications by constructing universal de Rham $F$ -gauges with $G$ -structure. We also study the cohomology of de Rham $F$ -gauges on these varieties. In particular, in the PEL-type case and when the weights of the flat automorphic vector bundles are $p$ -small, we determine the $F$ -gauge structure on their de Rham cohomology by the associated dual Bernstein-Gelfand-Gelfand (BGG) complexes.

Abstract Image

查看原文本刊更多论文

德朗F$ F$压力表和志村品种

研究了特征p$ p$的光滑代数变体的de Rham上同的F$ F$ -规。应用于Hodge型Shimura型的良好约简，我们通过构造具有G$ G$结构的通用de Rham F$ F$ -量规来恢复Ekedahl-Oort地层。我们还研究了德朗F$ F$量规在这些品种上的上同调性。特别地，在pel型情况下，当平面自同构向量束的权值为p$ p$ -小时，我们利用相关的对偶Bernstein-Gelfand-Gelfand （BGG）配合确定了它们在de Rham上同调上的F$ F$ -规范结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.