Berkovich spaces and applications [electronic resource] / Antoine Ducros, Charles Favre, Johannes Nicaise, editors.

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Berkovich spaces and applications [electronic resource] / Antoine Ducros, Charles Favre, Johannes Nicaise, editors.

9783319110295 electronic book
3319110292 electronic book
9783319110288

Cham : Springer, 2015.

English

1 online resource (xix, 413 pages) : illustrations.

10.1007/978-3-319-11029-5 doi

QA551

516.3/5

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.

Includes bibliographical references.

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Online resource; title from PDF title page (SpringerLink, viewed January 21, 2015).

Lecture notes in mathematics (Springer-Verlag) ; 2119.

Print version: 9783319110288

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