Berkovich Spaces and Applications

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Sprache: Englisch

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Beschreibung

We present an introduction to Berkovich¿s theory of non-archimedean analytic spaces that emphasizes its applications in various fields. The first part contains surveys of a foundational nature, including an introduction to Berkovich analytic spaces by M. Temkin, and to étale cohomology by A. Ducros, as well as a short note by C. Favre on the topology of some Berkovich spaces. The second part focuses on applications to geometry. A second text by A. Ducros contains a new proof of the fact that the higher direct images of a coherent sheaf under a proper map are coherent, and B. Rémy, A. Thuillier and A. Werner provide an overview of their work on the compactification of Bruhat-Tits buildings using Berkovich analytic geometry. The third and final part explores the relationship between non-archimedean geometry and dynamics. A contribution by M. Jonsson contains a thorough discussion of non-archimedean dynamical systems in dimension 1 and 2. Finally a survey by J.-P. Otal gives an account of Morgan-Shalen's theory of compactification of character varieties.
This book will provide the reader with enough material on the basic concepts and constructions related to Berkovich spaces to move on to more advanced research articles on the subject. We also hope that the applications presented here will inspire the reader to discover new settings where these beautiful and intricate objects might arise.

Zusammenfassung

An accessible introduction to the rapidly growing theory of Berkovich analytic spaces

Presents an original point of view, even on the basics of the theory

Gives an exposition of the striking applications of Berkovich theory to group theory and dynamics

Inhaltsverzeichnis

Introduction to Berkovich analytic spaces.- Etale cohomology of schemes and analytic spaces.- Countability properties of Berkovich spaces.- Cohomological finiteness of proper morphisms in algebraic geometry: a purely transcendental proof, without projective tools.- Bruhat-Tits buildings and analytic geometry.- Dynamics on Berkovich spaces in low dimensions.- Compactifications of spaces of representations (after Culler, Morgan and Shalen).

Details

Erscheinungsjahr:	2014
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Lecture Notes in Mathematics
Inhalt:	xix 413 S. 18 s/w Illustr. 413 p. 18 illus.
ISBN-13:	9783319110288
ISBN-10:	3319110284
Sprache:	Englisch
Herstellernummer:	86379741
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Redaktion:	Ducros, Antoine Nicaise, Johannes Favre, Charles
Herausgeber:	Antoine Ducros/Charles Favre/Johannes Nicaise
Hersteller:	Springer International Publishing Springer International Publishing AG Lecture Notes in Mathematics
Maße:	235 x 155 x 24 mm
Von/Mit:	Antoine Ducros (u. a.)
Erscheinungsdatum:	03.12.2014
Gewicht:	0,657 kg