Berkovich Spaces and Applications

Antoine Ducros, Charles Favre, Johannes Nicaise (Herausgeber)

Buch | Softcover

XIX, 413 Seiten

2014 | 2015
Springer International Publishing (Verlag)
978-3-319-11028-8 (ISBN)

Artikel merken

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.

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).

Erscheint lt. Verlag	3.12.2014
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XIX, 413 p. 18 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	664 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Berkovich analytic spaces • Bruhat-Tits buildings • Etale cohomology • Morgan-Shalen's compactification • Non-Archimedean dynamics
ISBN-10	3-319-11028-4 / 3319110284
ISBN-13	978-3-319-11028-8 / 9783319110288
Zustand	Neuware