Étale Cohomology of Rigid Analytic Varieties and Adic Spaces PDF Download

Author: Roland Huber
Publisher: Springer
ISBN: 3663099911
Category : Mathematics
Languages : en
Pages : 460

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Book Description
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

Author: Siegfried Bosch
Publisher: Springer
ISBN: 3319044176
Category : Mathematics
Languages : en
Pages : 255

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Book Description
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".

Author: Peter Scholze
Publisher: Princeton University Press
ISBN: 0691202095
Category : Mathematics
Languages : en
Pages : 260

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Book Description
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.

Author: Jean Fresnel
Publisher: Springer Science & Business Media
ISBN: 1461200415
Category : Mathematics
Languages : en
Pages : 303

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Book Description
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.

Author: Christopher Lazda
Publisher: Springer
ISBN: 331930951X
Category : Mathematics
Languages : en
Pages : 271

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Book Description
In this monograph, the authors develop a new theory of p-adic cohomology for varieties over Laurent series fields in positive characteristic, based on Berthelot's theory of rigid cohomology. Many major fundamental properties of these cohomology groups are proven, such as finite dimensionality and cohomological descent, as well as interpretations in terms of Monsky-Washnitzer cohomology and Le Stum's overconvergent site. Applications of this new theory to arithmetic questions, such as l-independence and the weight monodromy conjecture, are also discussed. The construction of these cohomology groups, analogous to the Galois representations associated to varieties over local fields in mixed characteristic, fills a major gap in the study of arithmetic cohomology theories over function fields. By extending the scope of existing methods, the results presented here also serve as a first step towards a more general theory of p-adic cohomology over non-perfect ground fields. Rigid Cohomology over Laurent Series Fields will provide a useful tool for anyone interested in the arithmetic of varieties over local fields of positive characteristic. Appendices on important background material such as rigid cohomology and adic spaces make it as self-contained as possible, and an ideal starting point for graduate students looking to explore aspects of the classical theory of rigid cohomology and with an eye towards future research in the subject.

Author: Kazuhiro Fujiwara
Publisher:
ISBN: 9783037196359
Category : MATHEMATICS
Languages : en
Pages : 863

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Book Description
Rigid geometry is one of the modern branches of algebraic and arithmetic geometry. It has its historical origin in J. Tate's rigid analytic geometry, which aimed at developing an analytic geometry over non-archimedean valued fields. Nowadays, rigid geometry is a discipline in its own right and has acquired vast and rich structures, based on discoveries of its relationship with birational and formal geometries. In this research monograph, foundational aspects of rigid geometry are discussed, putting emphasis on birational and topological features of rigid spaces. Besides the rigid geometry itself, topics include the general theory of formal schemes and formal algebraic spaces, based on a theory of complete rings which are not necessarily Noetherian. Also included is a discussion on the relationship with Tate's original rigid analytic geometry, V.G. Berkovich's analytic geometry and R. Huber's adic spaces. As a model example of applications, a proof of Nagata's compactification theorem for schemes is given in the appendix. The book is encyclopedic and almost self-contained.

Author: Bhargav Bhatt
Publisher: Springer Nature
ISBN: 3031215508
Category : Mathematics
Languages : en
Pages : 325

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Book Description
This proceedings volume contains articles related to the research presented at the 2019 Simons Symposium on p-adic Hodge theory. This symposium was focused on recent developments in p-adic Hodge theory, especially those concerning non-abelian aspects This volume contains both original research articles as well as articles that contain both new research as well as survey some of these recent developments.

Author: Siegfried Bosch
Publisher: Springer
ISBN: 9783642522314
Category : Mathematics
Languages : en
Pages : 436

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Book Description
: So eine Illrbeit witb eigentIid) nie rertig, man muli iie fur fertig erfHiren, wenn man nad) 8eit nnb Umftiinben bas moglid)fte get an qat. (@oetqe

Author: Vladimir G. Berkovich
Publisher: American Mathematical Soc.
ISBN: 0821890204
Category : Mathematics
Languages : en
Pages : 181

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Book Description
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.

Author: Bhargav Bhatt
Publisher: Springer Nature
ISBN: 3030438449
Category : Mathematics
Languages : en
Pages : 325

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Book Description
This proceedings volume contains articles related to the research presented at the 2017 Simons Symposium on p-adic Hodge theory. This symposium was focused on recent developments in p-adic Hodge theory, especially those concerning integral questions and their connections to notions in algebraic topology. This volume features original research articles as well as articles that contain new research and survey some of these recent developments. It is the first of three volumes dedicated to p-adic Hodge theory.