| Item type | Current location | Collection | Call number | Copy number | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
| E-Books | Biblioteca da FCTUNL | Não Ficção | QA564.SPR FCT 96697 (Browse shelf) | 1 | Available |
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| QA564.SPR FCT 96438 Rational points on elliptic curves | QA564.SPR FCT 96622 Mathematical concepts | QA564.SPR FCT 96652 Beauville surfaces and groups | QA564.SPR FCT 96697 Berkovich spaces and applications | QA564.SPR FCT 96732 Period mappings with applications to symplectic complex spaces | QA564.SPR FCT 96739 The Grassmannian variety | QA564.SPR FCT 96770 Ideals, varieties, and algorithms |
Colocação: Online
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.
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