$\text{GSp}_{2g}$与分支轨迹的尾数特征变异配对

IF 0.9 3区数学 Q2 MATHEMATICS

Documenta Mathematica Pub Date : 2020-05-10 DOI:10.4171/dm/826

Ju-Feng Wu

{"title":"$\\text{GSp}_{2g}$与分支轨迹的尾数特征变异配对","authors":"Ju-Feng Wu","doi":"10.4171/dm/826","DOIUrl":null,"url":null,"abstract":"In the present article, we study the overconvergent cohomology groups related to $\\text{GSp}_{2g}$. We construct a pairing on the cohomology groups. On the other hand, by considering the parabolic cohomology groups and applying the strategy in [JN19], we constructed the cuspidal eigenvariety for $\\text{GSp}_{2g}$. The pairing on the cohomology groups then induces a pairing on some coherent sheaves of the cuspidal eigenvariety. As an application, we follow the strategy in [Bel10, Chapter VI] to study the ramification locus of the cuspidal eigenvariety for $\\text{GSp}_{4}$ over the corresponding weight space.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2020-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"A pairing on the cuspidal eigenvariety for $\\\\text{GSp}_{2g}$ and the ramification locus\",\"authors\":\"Ju-Feng Wu\",\"doi\":\"10.4171/dm/826\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the present article, we study the overconvergent cohomology groups related to $\\\\text{GSp}_{2g}$. We construct a pairing on the cohomology groups. On the other hand, by considering the parabolic cohomology groups and applying the strategy in [JN19], we constructed the cuspidal eigenvariety for $\\\\text{GSp}_{2g}$. The pairing on the cohomology groups then induces a pairing on some coherent sheaves of the cuspidal eigenvariety. As an application, we follow the strategy in [Bel10, Chapter VI] to study the ramification locus of the cuspidal eigenvariety for $\\\\text{GSp}_{4}$ over the corresponding weight space.\",\"PeriodicalId\":50567,\"journal\":{\"name\":\"Documenta Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2020-05-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Documenta Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/dm/826\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Documenta Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/dm/826","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 4

摘要

在本文中，我们研究了$\text{GSp}_{2g}$相关的超收敛上同群。我们在上同调群上构造了一个对。另一方面，通过考虑抛物型上同群并应用[JN19]中的策略，我们构造了$\text{GSp}_{2g}$的倒态特征簇。在上同调群上的配对，进而推导出在倒轴特征变异的一些相干束上的配对。作为一个应用，我们遵循[Bel10, Chapter VI]中的策略，研究$\text{GSp}_{4}$在相应权空间上的倒角特征变分轨迹。

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

A pairing on the cuspidal eigenvariety for $\text{GSp}_{2g}$ and the ramification locus

In the present article, we study the overconvergent cohomology groups related to $\text{GSp}_{2g}$. We construct a pairing on the cohomology groups. On the other hand, by considering the parabolic cohomology groups and applying the strategy in [JN19], we constructed the cuspidal eigenvariety for $\text{GSp}_{2g}$. The pairing on the cohomology groups then induces a pairing on some coherent sheaves of the cuspidal eigenvariety. As an application, we follow the strategy in [Bel10, Chapter VI] to study the ramification locus of the cuspidal eigenvariety for $\text{GSp}_{4}$ over the corresponding weight space.

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

Documenta Mathematica 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： DOCUMENTA MATHEMATICA is open to all mathematical fields und internationally oriented Documenta Mathematica publishes excellent and carefully refereed articles of general interest, which preferably should rely only on refereed sources and references.