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Berkovich Spaces and Applications

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,...

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Corporate Author: SpringerLink (Online service)
Other Authors: Ducros, Antoine. (Editor, http://id.loc.gov/vocabulary/relators/edt), Favre, Charles. (Editor, http://id.loc.gov/vocabulary/relators/edt), Nicaise, Johannes. (Editor, http://id.loc.gov/vocabulary/relators/edt)
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
Edition:1st ed. 2015.
Series:Lecture Notes in Mathematics, 2119
Subjects:
Algebraic geometry.
Dynamics.
Ergodic theory.
Topological groups.
Lie groups.
Algebraic Geometry.
Dynamical Systems and Ergodic Theory.
Topological Groups, Lie Groups.
Online Access:https://doi.org/10.1007/978-3-319-11029-5
Table of Contents:
  • 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).

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