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Local systems in algebraic-arithmetic geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	Local systems in algebraic-arithmetic geometryby Helene Esnault.
Author:	Esnault, Helene.
Published:	Cham :Springer Nature Switzerland :2023.
Description:	vii, 94 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Geometry, Algebraic.
Online resource:	https://doi.org/10.1007/978-3-031-40840-3
ISBN:	9783031408403$q(electronic bk.)

Local systems in algebraic-arithmetic geometry
Esnault, Helene.

Local systems in algebraic-arithmetic geometry[electronic resource] /by Helene Esnault. - Cham :Springer Nature Switzerland :2023. - vii, 94 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23371617-9692 ;. - Lecture notes in mathematics ;2035..

The topological fundamental group of a smooth complex algebraic variety is poorly understood. One way to approach it is to consider its complex linear representations modulo conjugation, that is, its complex local systems. A fundamental problem is then to single out the complex points of such moduli spaces which correspond to geometric systems, and more generally to identify geometric subloci of the moduli space of local systems with special arithmetic properties. Deep conjectures have been made in relation to these problems. This book studies some consequences of these conjectures, notably density, integrality and crystallinity properties of some special loci. This monograph provides a unique compelling and concise overview of an active area of research and is useful to students looking to get into this area. It is of interest to a wide range of researchers and is a useful reference for newcomers and experts alike.

ISBN: 9783031408403$q(electronic bk.)

Standard No.: 10.1007/978-3-031-40840-3doiSubjects--Topical Terms:

190843
Geometry, Algebraic.

LC Class. No.: QA564

Dewey Class. No.: 516.35

Local systems in algebraic-arithmetic geometry
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520 $a The topological fundamental group of a smooth complex algebraic variety is poorly understood. One way to approach it is to consider its complex linear representations modulo conjugation, that is, its complex local systems. A fundamental problem is then to single out the complex points of such moduli spaces which correspond to geometric systems, and more generally to identify geometric subloci of the moduli space of local systems with special arithmetic properties. Deep conjectures have been made in relation to these problems. This book studies some consequences of these conjectures, notably density, integrality and crystallinity properties of some special loci. This monograph provides a unique compelling and concise overview of an active area of research and is useful to students looking to get into this area. It is of interest to a wide range of researchers and is a useful reference for newcomers and experts alike.
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