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Lecture Notes in Mathematics

Berkovich Spaces and Applications

Editors: Ducros, Antoine, Favre, Charles, Nicaise, Johannes (Eds.)

  • 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
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eBook 53,54 €
price for Spain (gross)
  • ISBN 978-3-319-11029-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 67,59 €
price for Spain (gross)
  • ISBN 978-3-319-11028-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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. 
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.

Table of contents (7 chapters)

  • Introduction to Berkovich Analytic Spaces

    Temkin, Michael

    Pages 3-66

    Preview Buy Chapter 30,19 €
  • Étale Cohomology of Schemes and Analytic Spaces

    Ducros, Antoine

    Pages 67-118

    Preview Buy Chapter 30,19 €
  • Countability Properties of Some Berkovich Spaces

    Favre, Charles

    Pages 119-132

    Preview Buy Chapter 30,19 €
  • Cohomological Finiteness of Proper Morphisms in Algebraic Geometry: A Purely Transcendental Proof, Without Projective Tools

    Ducros, Antoine

    Pages 135-140

    Preview Buy Chapter 30,19 €
  • Bruhat-Tits Buildings and Analytic Geometry

    Rémy, Bertrand (et al.)

    Pages 141-202

    Preview Buy Chapter 30,19 €

Buy this book

eBook 53,54 €
price for Spain (gross)
  • ISBN 978-3-319-11029-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 67,59 €
price for Spain (gross)
  • ISBN 978-3-319-11028-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Berkovich Spaces and Applications
Editors
  • Antoine Ducros
  • Charles Favre
  • Johannes Nicaise
Series Title
Lecture Notes in Mathematics
Series Volume
2119
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-11029-5
DOI
10.1007/978-3-319-11029-5
Softcover ISBN
978-3-319-11028-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIX, 413
Number of Illustrations and Tables
18 b/w illustrations
Topics