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.
Lectures on Formal and Rigid Geometry
Title | Lectures on Formal and Rigid Geometry PDF eBook |
Author | Siegfried Bosch |
Publisher | Springer |
Pages | 255 |
Release | 2014-08-22 |
Genre | Mathematics |
ISBN | 3319044176 |
The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".
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 |
Non-Archimedean Analysis
Title | Non-Archimedean Analysis PDF eBook |
Author | Siegfried Bosch |
Publisher | Springer |
Pages | 436 |
Release | 2012-06-28 |
Genre | Mathematics |
ISBN | 9783642522314 |
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Berkeley Lectures on P-adic Geometry
Title | Berkeley Lectures on P-adic Geometry PDF eBook |
Author | Peter Scholze |
Publisher | Princeton University Press |
Pages | 260 |
Release | 2020-05-26 |
Genre | Mathematics |
ISBN | 0691202095 |
Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field. This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.