Local systems in algebraic-arithmetic geometry / Hélène Esnault.

Format:

Book

Author/Creator:

Esnault, Hélène, 1953- Author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 volume 2337.

Lecture notes in mathematics, 0075-8434 ; volume 2337

Language:

English

Subjects (All):

Geometry, Algebraic.

Physical Description:

vii, 91 pages ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer, [2023]

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 rese\archers and is a useful reference for newcomers and experts alike."-- Back cover.

Contents:

Lecture 1: General Introduction

Lecture 2: Kronecker's Rationality Criteria and Grothendieck's p-Curvature Conjecture

Lecture 3: Malčev-Grothendieck's Theorem, Its Variants in Characteristic p>0, Gieseker's Conjecture, de Jong's Conjecture, and the One to Come

Lecture 4: Interlude on Some Similarity Between the Fundamental Groups in Characteristic 0 and p>0

Lecture 5: Interlude on Some Difference Between the Fundamental Groups in Characteristic 0 and p>0

Lecture 6: Density of Special Loci

Lecture 7: Companions, Integrality of Cohomologically Rigid Local Systems and of the Betti Moduli Space

Lecture 8: Rigid Local Systems and F-Isocrystals

Lecture 9: Rigid Local Systems, Fontaine-Laffaille Modules and Crystalline Local Systems

Lecture 10: Comments and Questions.

Notes:

Includes bibliographical references (pages 87-91).

ISBN:

9783031408397

303140839X

OCLC:

1403128645