Lectures on Formal and Rigid Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Formal and Rigid Geometry write by Siegfried Bosch. This book was released on 2014-08-22. Lectures on Formal and Rigid Geometry available 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".
Rigid Geometry of Curves and Their Jacobians
Rigid Geometry of Curves and Their Jacobians - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Rigid Geometry of Curves and Their Jacobians write by Werner Lütkebohmert. This book was released on 2016-01-26. Rigid Geometry of Curves and Their Jacobians available in PDF, EPUB and Kindle. 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.
Foundations of Rigid Geometry I
Foundations of Rigid Geometry I - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Rigid Geometry I write by Kazuhiro Fujiwara. This book was released on 2018. Foundations of Rigid Geometry I available 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.
$p$-adic Geometry
$p$-adic Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook $p$-adic Geometry write by Matthew Baker. This book was released on 2008. $p$-adic Geometry available in PDF, EPUB and Kindle. "In recent decades, p-adic geometry and p-adic cohomology theories have become indispensable tools in number theory, algebraic geometry, and the theory of automorphic representations. The Arizona Winter Schoo1 2007, on which the current book is based, was a unique opportunity to introduce graduate students to this subject." "Following invaluable introductions by John Tate and Vladimir Berkovich, two pioneers of non-archimedean geometry, Brian Conrad's chapter introduces the general theory of Tate's rigid analytic spaces, Raynaud's view of them as the generic fibers of formal schemes, and Berkovich spaces. Samit Dasgupta and Jeremy Teitelbaum discuss the p-adic upper half plane as an example of a rigid analytic space and give applications to number theory (modular forms and the p-adic Langlands program). Matthew Baker offers a detailed discussion of the Berkovich projective line and p-adic potential theory on that and more general Berkovich curves. Finally, Kiran Kedlaya discusses theoretical and computational aspects of p-adic cohomology and the zeta functions of varieties. This book will be a welcome addition to the library of any graduate student and researcher who is interested in learning about the techniques of p-adic geometry."--BOOK JACKET.
Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 1
Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 1 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 1 write by Raf Cluckers. This book was released on 2011-09-22. Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 1 available 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.
