Etale Cohomology for Non-archimedean Analytic Spaces
Title | Etale Cohomology for Non-archimedean Analytic Spaces PDF eBook |
Author | Vladimir G. Berkovichm |
Publisher | |
Pages | 161 |
Release | 1993 |
Genre | Analytic spaces |
ISBN |
Etale cohomology for non-Archimedean analytic spaces
Title | Etale cohomology for non-Archimedean analytic spaces PDF eBook |
Author | Vladimir G. Berkovich |
Publisher | |
Pages | 232 |
Release | 1993 |
Genre | Analytic spaces |
ISBN |
Berkovich Spaces and Applications
Title | Berkovich Spaces and Applications PDF eBook |
Author | Antoine Ducros |
Publisher | Springer |
Pages | 432 |
Release | 2014-11-21 |
Genre | Mathematics |
ISBN | 3319110292 |
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.
Spectral Theory and Analytic Geometry over Non-Archimedean Fields
Title | Spectral Theory and Analytic Geometry over Non-Archimedean Fields PDF eBook |
Author | Vladimir G. Berkovich |
Publisher | American Mathematical Soc. |
Pages | 181 |
Release | 2012-08-02 |
Genre | Mathematics |
ISBN | 0821890204 |
The purpose of this book is to introduce a new notion of analytic space over a non-Archimedean field. Despite the total disconnectedness of the ground field, these analytic spaces have the usual topological properties of a complex analytic space, such as local compactness and local arcwise connectedness. This makes it possible to apply the usual notions of homotopy and singular homology. The book includes a homotopic characterization of the analytic spaces associated with certain classes of algebraic varieties and an interpretation of Bruhat-Tits buildings in terms of these analytic spaces. The author also studies the connection with the earlier notion of a rigid analytic space. Geometrical considerations are used to obtain some applications, and the analytic spaces are used to construct the foundations of a non-Archimedean spectral theory of bounded linear operators. This book requires a background at the level of basic graduate courses in algebra and topology, as well as some familiarity with algebraic geometry. It would be of interest to research mathematicians and graduate students working in algebraic geometry, number theory, and -adic analysis.
Étale Cohomology of Rigid Analytic Varieties and Adic Spaces
Title | Étale Cohomology of Rigid Analytic Varieties and Adic Spaces PDF eBook |
Author | Roland Huber |
Publisher | Springer |
Pages | 460 |
Release | 2013-07-01 |
Genre | Mathematics |
ISBN | 3663099911 |
Diese Forschungsmonographie von hohem mathematischen Niveau liefert einen neuen Zugang zu den rigid-analytischen Räumen, sowie ihrer etalen Kohomologie.USP: Aus der Froschung: Zahlentheorie und Algebraische Geometrie
Étale Cohomology of Rigid Analytic Spaces
Title | Étale Cohomology of Rigid Analytic Spaces PDF eBook |
Author | A. J. Jong |
Publisher | |
Pages | 62 |
Release | 1995 |
Genre | |
ISBN |
Rigid Analytic Geometry and Its Applications
Title | Rigid Analytic Geometry and Its Applications PDF eBook |
Author | Jean Fresnel |
Publisher | Springer Science & Business Media |
Pages | 303 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461200415 |
Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "points of rigid spaces," étale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology. The exposition is concise, self-contained, rich in examples and exercises, and will serve as an excellent graduate-level text for the classroom or for self-study.