Foundations Of Rigid Geometry
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Foundations Of Rigid Geometry I
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Author : Kazuhiro Fujiwara
language : en
Publisher:
Release Date : 2018
Foundations Of Rigid Geometry I written by Kazuhiro Fujiwara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with MATHEMATICS categories.
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.
Foundations Of Rigid Geometry
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Author : Kazuhiro Fujiwara
language : en
Publisher:
Release Date : 2018
Foundations Of Rigid Geometry written by Kazuhiro Fujiwara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Rigid Geometry Of Curves And Their Jacobians
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Author : Werner Lütkebohmert
language : en
Publisher: Springer
Release Date : 2016-02-03
Rigid Geometry Of Curves And Their Jacobians written by Werner Lütkebohmert and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-03 with Mathematics categories.
This book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail. Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.
Lectures On Formal And Rigid Geometry
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Author : Siegfried Bosch
language : en
Publisher: Springer
Release Date : 2014-08-22
Lectures On Formal And Rigid Geometry written by Siegfried Bosch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-22 with Mathematics categories.
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".
Rigid Analytic Geometry And Its Applications
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Author : Jean Fresnel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Rigid Analytic Geometry And Its Applications written by Jean Fresnel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Foundations Of Algebraic Geometry 29
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Author : André 1906- Weil
language : en
Publisher: Hassell Street Press
Release Date : 2021-09-10
Foundations Of Algebraic Geometry 29 written by André 1906- Weil and has been published by Hassell Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-10 with categories.
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Foundations Of Geometry
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Author : C. R. Wylic
language : en
Publisher:
Release Date : 1960
Foundations Of Geometry written by C. R. Wylic and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with categories.
Almost Ring Theory
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Author : Ofer Gabber
language : en
Publisher: Springer Science & Business Media
Release Date : 2003
Almost Ring Theory written by Ofer Gabber and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Arithmetical algebraic geometry categories.
Spectral Theory And Analytic Geometry Over Non Archimedean Fields
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Author : Vladimir G. Berkovich
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-08-02
Spectral Theory And Analytic Geometry Over Non Archimedean Fields written by Vladimir G. Berkovich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-02 with Mathematics categories.
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.
The Foundations Of Geometry And The Non Euclidean Plane
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Author : George Edward Martin
language : en
Publisher:
Release Date : 1982
The Foundations Of Geometry And The Non Euclidean Plane written by George Edward Martin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.