Monodromy of Airy and Kloosterman sheaves
type: Item
instance of: scholarly article
title: Monodromy of Airy and Kloosterman sheaves
zbMATH Open document ID: 0976.14017
DOI: 10.1215/S0012-7094-00-10332-8
author: Ondrej Šuch
published in: Duke Mathematical Journal
publication date: 2001-12-27T00:00:00Z
review text: A useful tool to study a family of curves is the geometric monodromy group \(G\). Using Fourier transforms the author essentially proves the following three theorems: For any \(g\geq 3\), the geometric monodromy group of hyperelliptic curves of genus \(g\) and \(2\)-rank zero over \(\overline{\mathbb{F}_2}\) is \(Sp(2g)\). If \(p>2\), and \(\mathcal F\) is a Lie irreducible Airy sheaf over \(A^1\otimes\overline{\mathbb{F}_p}\), then the Lie algebra of \(G\) is \(sl\) or \(sp\) in its standard representation. Let \(\mathcal F\) be a Lie irreducible Kloosterman sheaf on \(A^1\) over \(\overline{\mathbb{F}_p}\). If \(p>\sqrt{\text{rank }{\mathcal F}+1}\), then the Lie algebra of \(G\) is either \(sl\) or \(sp\) or \(so\) in its standard representation.
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14G15
zbMATH DE Number: 1491011
zbMATH Keywords: hyperelliptic curves
zbMATH Keywords: family of curves
zbMATH Keywords: filtrations
zbMATH Keywords: geometric monodromy group
zbMATH Keywords: Fourier transforms
zbMATH Keywords: Airy sheaf
zbMATH Keywords: Kloosterman sheaf
reviewed by: Antonio Cossidente
MaRDI profile type: Publication
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full work available at URL: s0012-7094-00-10332-8
OpenAlex ID: W1559621401
description: scientific article; zbMATH DE number 1491011