Foundations Of Rigid Geometry I PDF Download
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Author | : Kazuhiro Fujiwara |
Publisher | : |
Total Pages | : 863 |
Release | : 2018 |
Genre | : MATHEMATICS |
ISBN | : 9783037196359 |
Download Foundations of Rigid Geometry I Book in PDF, ePub and Kindle
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 | : Kazuhiro Fujiwara |
Publisher | : |
Total Pages | : 0 |
Release | : 2018 |
Genre | : |
ISBN | : |
Download Foundations of Rigid Geometry Book in PDF, ePub and Kindle
Author | : Siegfried Bosch |
Publisher | : Springer |
Total Pages | : 254 |
Release | : 2014-08-22 |
Genre | : Mathematics |
ISBN | : 3319044176 |
Download Lectures on Formal and Rigid Geometry Book in PDF, ePub and Kindle
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 | : Jean Fresnel |
Publisher | : Springer Science & Business Media |
Total Pages | : 303 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461200415 |
Download Rigid Analytic Geometry and Its Applications Book in PDF, ePub and Kindle
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 | : André Weil |
Publisher | : |
Total Pages | : 363 |
Release | : 1946 |
Genre | : Geometry, Algebraic |
ISBN | : 9781470431761 |
Download Foundations of Algebraic Geometry Book in PDF, ePub and Kindle
This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Author | : Ofer Gabber |
Publisher | : Springer Science & Business Media |
Total Pages | : 324 |
Release | : 2003 |
Genre | : Arithmetical algebraic geometry |
ISBN | : 9783540405948 |
Download Almost Ring Theory Book in PDF, ePub and Kindle
Author | : Raf Cluckers |
Publisher | : Cambridge University Press |
Total Pages | : 347 |
Release | : 2011-09-22 |
Genre | : Mathematics |
ISBN | : 1139499793 |
Download Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 1 Book in PDF, ePub and Kindle
Assembles different theories of motivic integration for the first time, providing all of the necessary background for graduate students and researchers from algebraic geometry, model theory and number theory. In a rapidly-evolving area of research, this volume and Volume 2, which unite the several viewpoints and applications, will prove invaluable.
Author | : Vladimir G. Berkovich |
Publisher | : American Mathematical Soc. |
Total Pages | : 181 |
Release | : 2012-08-02 |
Genre | : Mathematics |
ISBN | : 0821890204 |
Download Spectral Theory and Analytic Geometry over Non-Archimedean Fields Book in PDF, ePub and Kindle
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 | : Christopher Lazda |
Publisher | : Springer |
Total Pages | : 267 |
Release | : 2016-04-27 |
Genre | : Mathematics |
ISBN | : 331930951X |
Download Rigid Cohomology over Laurent Series Fields Book in PDF, ePub and Kindle
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 | : Tim Maudlin |
Publisher | : Oxford University Press |
Total Pages | : 374 |
Release | : 2014-02 |
Genre | : Mathematics |
ISBN | : 0198701306 |
Download New Foundations for Physical Geometry Book in PDF, ePub and Kindle
Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.