The purity locus of matrix Kloosterman sums

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2024-02-29 DOI:10.1090/tran/9149

Márton Erdélyi, Will Sawin, Árpád Tóth

引用次数: 0

Abstract

We construct a perverse sheaf related to the the matrix exponential sums investigated by Erdélyi and Tóth [Matrix Kloosterman sums, 2021, arXiv:2109.00762]. As this sheaf appears as a summand of certain tensor product of Kloosterman sheaves, we can establish the exact structure of the cohomology attached to the sums by relating it to the Springer correspondence and using the recursion formula of Erdélyi and Tóth.

查看原文本刊更多论文

矩阵克罗斯特曼和的纯度位置

我们构建了一个与埃尔德利和托特研究的矩阵指数和相关的反剪[矩阵克罗斯特曼和，2021，arXiv:2109.00762]。由于这个 sheaf 是作为 Kloosterman sheaves 的某些张量积的和出现的，我们可以通过将其与 Springer 对应关系联系起来，并使用 Erdélyi 和 Tóth 的递推公式，来建立与和相关的同调的精确结构。

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

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.