Local Systems in Algebraic-Arithmetic Geometry

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...

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Bibliographic Details
Main Author Esnault, Hélène
Format eBook
LanguageEnglish
Published Cham Springer 2023
Springer Nature Switzerland
Edition1
SeriesLecture Notes in Mathematics
Subjects
Algebraic Geometry
Geometry, Algebraic
Mathematics
Mathematics and Statistics
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Summary: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:9783031408397
303140839X
ISSN:0075-8434
1617-9692
DOI:10.1007/978-3-031-40840-3