Overview
- 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
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2119)
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Table of contents (7 chapters)
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Front Matter
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Berkovich Analytic Spaces
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Front Matter
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Valuation Spaces and Dynamics
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Front Matter
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Back Matter
Keywords
About this book
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.Â
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.
Editors and Affiliations
Bibliographic Information
Book Title: Berkovich Spaces and Applications
Editors: Antoine Ducros, Charles Favre, Johannes Nicaise
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-11029-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Softcover ISBN: 978-3-319-11028-8Published: 03 December 2014
eBook ISBN: 978-3-319-11029-5Published: 21 November 2014
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIX, 413
Number of Illustrations: 18 b/w illustrations
Topics: Algebraic Geometry, Dynamical Systems and Ergodic Theory, Topological Groups, Lie Groups