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Local systems in algebraic-arithmetic geometry / Hélène Esnault.

1st ed. 2023.

9783031408403 (electronic bk.)
3031408403 (electronic bk.)
9783031408397

Cham, Switzerland : Springer, [2023]

English

1 online resource (vii, 94 pages) : black and white illustrations.

10.1007/978-3-031-40840-3 doi

QA564

516.3/5

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 rese\archers and is a useful reference for newcomers and experts alike.

Includes bibliographical references.

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Online resource; title from PDF title page (SpringerLink, viewed September 26, 2023).

Lecture notes in mathematics (Springer-Verlag) ; 2337.

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