Berkovich spaces and applications / Antoine Ducros, Charles Favre, Johannes Nicaise, editors.

Contributor(s):

Material type: Text

TextSeries: Lecture notes in mathematics (Springer-Verlag) ; 2119.Publisher: Cham : Springer, 2015Description: 1 online resource (xix, 413 pages) : illustrationsContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9783319110295
3319110292
3319110284
9783319110288

Subject(s): Additional physical formats: Printed edition:: No titleDDC classification:

516.3/5 23

LOC classification:

QA551

Online resources:

Click here to access online

Contents:

Introduction to Berkovich analytical spaces - Cohomology of schemes and Etale analytical spaces - Accounting properties of Berkovich spaces - Cohomological finitude of proper morphisms in algebraic geometry: a purely transcendental proof, without projective tools - Bruhat-Tits buildings and Analytical geometry - - Dynamics on Berkovich spaces in low dimensions - Compactifications of representation spaces (according to Culler, Morgan and Shalen).

Summary: We present an introduction to Berkovich's theory of non-Archimedean analytical spaces that emphasizes its applications in various fields. The first part contains studies of a foundational nature, including an introduction to analytic Berkovich spaces by M. Temkin and to étale cohomology by A. Ducros, as well as a brief 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 new proof of the fact that the upper direct images of a coherent beam under a suitable map are coherent, and B. Rémy, A. Thuillier and A. Werner give an overview of their work on Bruhat-Tits building compaction using Berkovich analytical geometry. The third and final part explores the relationship between non-Archimedean geometry and dynamics. A contribution by M. Jonsson contains an exhaustive discussion of non-Archimedean dynamical systems in dimensions 1 and 2. Finally, a study by J.-P. Otal gives an account of the Morgan-Shalen theory on the compactification of manifolds of characters. 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 topic. We also hope that the applications presented here inspire the reader to discover new scenarios where these beautiful and intricate objects could arise.

Holdings ( 1 )
Title notes ( 5 )

Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
eBook	e-Library	eBook LN Mathematic		Available

Total holds: 0

Includes bibliographical references.

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

We present an introduction to Berkovich's theory of non-Archimedean analytical spaces that emphasizes its applications in various fields. The first part contains studies of a foundational nature, including an introduction to analytic Berkovich spaces by M. Temkin and to étale cohomology by A. Ducros, as well as a brief 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 new proof of the fact that the upper direct images of a coherent beam under a suitable map are coherent, and B. Rémy, A. Thuillier and A. Werner give an overview of their work on Bruhat-Tits building compaction using Berkovich analytical geometry. The third and final part explores the relationship between non-Archimedean geometry and dynamics. A contribution by M. Jonsson contains an exhaustive discussion of non-Archimedean dynamical systems in dimensions 1 and 2. Finally, a study by J.-P. Otal gives an account of the Morgan-Shalen theory on the compactification of manifolds of characters. 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 topic. We also hope that the applications presented here inspire the reader to discover new scenarios where these beautiful and intricate objects could arise.

English.