Local Systems in Algebraic-Arithmetic Geometry

Häftad, Engelska, 2023

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The topological fundamental group of a smooth complex algebraic variety is poorly understood. 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.

Produktinformation

Utgivningsdatum2023-09-20
Mått155 x 235 x 7 mm
Vikt172 g
FormatHäftad
SpråkEngelska
SerieLecture Notes in Mathematics
Antal sidor94
FörlagSpringer International Publishing AG
ISBN9783031408397

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Matematik inom Naturvetenskap och teknik

Hélène Esnault is an emeritus Einstein Professor at the Freie Universität Berlin. She is currently a part time Professor at the University of Copenhagen and an associate part time Professor at Harvard University. She is working in the field of algebraic and arithmetic geometry. She established bridges between the analytic and arithmetic theories comprising for example the study of vanishing theorems, of rational points over finite fields, of complex and l-adic local systems, of analytic and arithmetic crystals, of algebraic cycles. She was awarded numerous prizes, including the Cantor medal (2019), and several honorary degrees, including the one of the University of Chicago (2023) for her "vision of algebraic geometry that touches upon most of the active branches of that vast field but is nevertheless recognizable her own."

- 1. Lecture 1: General Introduction. - 2. Lecture 2: Kronecker’s Rationality Criteria and Grothendieck’s p-Curvature Conjecture. - 3. Lecture 3: Malčev-Grothendieck’s Theorem, Its Variants in Characteristic p > 0, Gieseker’s Conjecture, de Jong’s Conjecture, and the One to Come. - 4. Lecture 4: Interlude on Some Similarity Between the Fundamental Groups in Characteristic 0 and p > 0. - 5. Lecture 5: Interlude on Some Difference Between the Fundamental Groups in Characteristic 0 and p > 0. - 6. Lecture 6: Density of Special Loci. - 7. Lecture 7: Companions, Integrality of Cohomologically Rigid Local Systems and of the Betti Moduli Space. - 8. Lecture 8: Rigid Local Systems and F-Isocrystals. - 9. Lecture 9: Rigid Local Systems, Fontaine-Laffaille Modules and Crystalline Local Systems. - 10. Lecture 10: Comments and Questions.

“This book is based on a series of lectures delivered by the author on local systems in algebraic and arithmetic geometry. … the main theorems in this book are present in the original literature, the author often outlines the original proofs or presents simplified versions, making the material more accessible. This book is quite valuable for both researchers in the field and those with a general interest in the topic.” (XiaoWen Hu, Mathematical Reviews, May, 2025)