Vanishing linear periods of cuspidal automorphic sheaves for \(\mathrm{GL}_{m+n}\)
type: Item
instance of: scholarly article
title: Vanishing linear periods of cuspidal automorphic sheaves for \(\mathrm{GL}_{m+n}\)
author: Fang Shi
published in: Proceedings of the American Mathematical Society
publication date: 2024-06-13T00:00:00Z
review text: Let \(X\) stand for a connected smooth projective curve over an algebraically closed field with genus greater than one. Let \(E\) stand for an irreducible local system of rank \(m + n\) over \(X\). We denote by \(\mathrm{Per}_E\) the linear period of \(\mathrm{Aut}_E\), the automorphic \(E\)-Hecke eigensheaf on the stack classifying rank \(m + n\) vector bundles on \(X\).\N\NIn the paper under the review, the author shows that if \(m \neq n\) and \(m, n \geq 1\), then all cohomology sheaves of \(\mathrm{Per}_E\) vanish.
reviewed by: Ivan Matić
Mathematics Subject Classification ID: 11R39
Mathematics Subject Classification ID: 11S37
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 14H60
zbMATH DE Number: 7864460
zbMATH Keywords: linear periods
zbMATH Keywords: cuspidal automorphic sheaves
zbMATH Keywords: general linear groups
MaRDI profile type: Publication
cites work: Correspondance de Langlands géométrique pour les corps de fonctions. (Geometric Langlands correspondence for function fields)
cites work: On the geometric Langlands conjecture
cites work: On a vanishing conjecture appearing in the geometric Langlands correspondence
cites work: Linear periods.
cites work: Linear Periods of Automorphic Sheaves for GL2n
cites work: Local geometrized Rankin-Selberg method for \(\text{GL}(n\)).
DOI: 10.1090/PROC/16836
description: scientific article; zbMATH DE number 7864460