Berkovich Spaces and Applications

• Corporate Author: SpringerLink (Online service)
• Other Authors: Ducros, Antoine (Editor), Favre, Charles (Editor), Nicaise, Johannes (Editor)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Series: Lecture Notes in Mathematics, 2119
• Subjects: Mathematics.; Algebraic geometry.; Topological groups.; Lie groups.; Dynamics.; Ergodic theory.; Algebraic Geometry.; Dynamical Systems and Ergodic Theory.; Topological Groups, Lie Groups.

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,...

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).