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Cohomology Of Drinfeld Modular Varieties
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Book Synopsis Cohomology of Drinfeld Modular Varieties, Part 2, Automorphic Forms, Trace Formulas and Langlands Correspondence by :
Download or read book Cohomology of Drinfeld Modular Varieties, Part 2, Automorphic Forms, Trace Formulas and Langlands Correspondence written by and published by Cambridge University Press. This book was released on with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Cohomology of Drinfeld Modular Varieties by : Gérard Laumon
Download or read book Cohomology of Drinfeld Modular Varieties written by Gérard Laumon and published by . This book was released on 1996 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Cohomology of Drinfeld Modular Varieties by : Gérard Laumon
Download or read book Cohomology of Drinfeld Modular Varieties written by Gérard Laumon and published by . This book was released on 1996 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis by : Gérard Laumon
Download or read book Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis written by Gérard Laumon and published by Cambridge University Press. This book was released on 2010-12-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology of Drinfeld Modular Varieties aims to provide an introduction to both the subject of the title and the Langlands correspondence for function fields. These varieties are the analogs for function fields of Shimura varieties over number fields. This present volume is devoted to the geometry of these varieties and to the local harmonic analysis needed to compute their cohomology. To keep the presentation as accessible as possible, the author considers the simpler case of function rather than number fields; nevertheless, many important features can still be illustrated. It will be welcomed by workers in number theory and representation theory.
Book Synopsis Cohomology of Drinfeld Modular Varieties by : Gérard Laumon
Download or read book Cohomology of Drinfeld Modular Varieties written by Gérard Laumon and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis by : Gérard Laumon
Download or read book Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis written by Gérard Laumon and published by Cambridge University Press. This book was released on 2010-12-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology of Drinfeld Modular Varieties aims to provide an introduction to both the subject of the title and the Langlands correspondence for function fields. These varieties are the analogs for function fields of Shimura varieties over number fields. This present volume is devoted to the geometry of these varieties and to the local harmonic analysis needed to compute their cohomology. To keep the presentation as accessible as possible, the author considers the simpler case of function rather than number fields; nevertheless, many important features can still be illustrated. It will be welcomed by workers in number theory and representation theory.
Book Synopsis Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis by : Gérard Laumon
Download or read book Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis written by Gérard Laumon and published by Cambridge University Press. This book was released on 1996 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1995, Cohomology of Drinfeld Modular Varieties aimed to provide an introduction, in two volumes, both to this subject and to the Langlands correspondence for function fields. These varieties are the analogues for function fields of the Shimura varieties over number fields. The Langlands correspondence is a conjectured link between automorphic forms and Galois representations over a global field. By analogy with the number-theoretic case, one expects to establish the conjecture for function fields by studying the cohomology of Drinfeld modular varieties, which has been done by Drinfeld himself for the rank two case. The present volume is devoted to the geometry of these varieties, and to the local harmonic analysis needed to compute their cohomology. Though the author considers only the simpler case of function rather than number fields, many important features of the number field case can be illustrated.
Book Synopsis Cohomology of Drinfeld Modular Varieties, Part 2, Automorphic Forms, Trace Formulas and Langlands Correspondence by : Gérard Laumon
Download or read book Cohomology of Drinfeld Modular Varieties, Part 2, Automorphic Forms, Trace Formulas and Langlands Correspondence written by Gérard Laumon and published by Cambridge University Press. This book was released on 1997-01-09 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology of Drinfeld Modular Varieties aims to provide an introduction to this subject and to the Langlands correspondence for function fields. These varieties are the analogues for function fields of the Shimura varieties over number fields. The Langlands correspondence is a conjectured link between automorphic forms and Galois representations over a global field. By analogy with the number-theoretic case, one expects to establish the conjecture for function fields by studying the cohomology of Drinfeld modular varieties, which has been done by Drinfeld himself for the rank two case. This second volume is concerned with the ArthurSHSelberg trace formula, and to the proof in some cases of the Ramanujan-Petersson conjecture and the global Langlands conjecture for function fields. The author uses techniques that are extensions of those used to study Shimura varieties. Though the author considers only the simpler case of function rather than number fields, many important features of the number field case can be illustrated. Several appendices on background material keep the work reasonably self-contained. This book will be of much interest to all researchers in algebraic number theory and representation theory.
Book Synopsis Cohomology with Compact Supports of Drinfeld Modular Varieties by : G. Laumon
Download or read book Cohomology with Compact Supports of Drinfeld Modular Varieties written by G. Laumon and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Cohomology with Compact Supports of Drinfeld Modular Varieties by : Gérard Laumon
Download or read book Cohomology with Compact Supports of Drinfeld Modular Varieties written by Gérard Laumon and published by . This book was released on 1994 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Cohomology with Compact Supports of Drinfeld Modular Varieties by : Gérard Laumon
Download or read book Cohomology with Compact Supports of Drinfeld Modular Varieties written by Gérard Laumon and published by . This book was released on 1991 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Cohomology with Compact Supports of Drinfeld Modular Varieties by : Gérard Laumon
Download or read book Cohomology with Compact Supports of Drinfeld Modular Varieties written by Gérard Laumon and published by . This book was released on 1991 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Drinfeld Modules by : Mihran Papikian
Download or read book Drinfeld Modules written by Mihran Papikian and published by Springer Nature. This book was released on 2023-03-31 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers an introduction to the theory of Drinfeld modules, mathematical objects that are fundamental to modern number theory. After the first two chapters conveniently recalling prerequisites from abstract algebra and non-Archimedean analysis, Chapter 3 introduces Drinfeld modules and the key notions of isogenies and torsion points. Over the next four chapters, Drinfeld modules are studied in settings of various fields of arithmetic importance, culminating in the case of global fields. Throughout, numerous number-theoretic applications are discussed, and the analogies between classical and function field arithmetic are emphasized. Drinfeld Modules guides readers from the basics to research topics in function field arithmetic, assuming only familiarity with graduate-level abstract algebra as prerequisite. With exercises of varying difficulty included in each section, the book is designed to be used as the primary textbook for a graduate course on the topic, and may also provide a supplementary reference for courses in algebraic number theory, elliptic curves, and related fields. Furthermore, researchers in algebra and number theory will appreciate it as a self-contained reference on the topic.
Book Synopsis Compactification of the Drinfeld Modular Surfaces by : Thomas Lehmkuhl
Download or read book Compactification of the Drinfeld Modular Surfaces written by Thomas Lehmkuhl and published by American Mathematical Soc.. This book was released on 2009-01-21 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article the author describes in detail a compactification of the moduli schemes representing Drinfeld modules of rank 2 endowed with some level structure. The boundary is a union of copies of moduli schemes for Drinfeld modules of rank 1, and its points are interpreted as Tate data. The author also studies infinitesimal deformations of Drinfeld modules with level structure.
Book Synopsis Rational and Nearly Rational Varieties by : János Kollár
Download or read book Rational and Nearly Rational Varieties written by János Kollár and published by Cambridge University Press. This book was released on 2004-04-22 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most basic algebraic varieties are the projective spaces, and rational varieties are their closest relatives. In many applications where algebraic varieties appear in mathematics and the sciences, we see rational ones emerging as the most interesting examples. The authors have given an elementary treatment of rationality questions using a mix of classical and modern methods. Arising from a summer school course taught by János Kollár, this book develops the modern theory of rational and nearly rational varieties at a level that will particularly suit graduate students. There are numerous examples and exercises, all of which are accompanied by fully worked out solutions, that will make this book ideal as the basis of a graduate course. It will act as a valuable reference for researchers whilst helping graduate students to reach the point where they can begin to tackle contemporary research problems.
Book Synopsis Drinfeld Modules, Modular Schemes And Applications by : M Van Der Put
Download or read book Drinfeld Modules, Modular Schemes And Applications written by M Van Der Put and published by World Scientific. This book was released on 1997-08-27 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his 1974 seminal paper 'Elliptic modules', V G Drinfeld introduced objects into the arithmetic geometry of global function fields which are nowadays known as 'Drinfeld Modules'. They have many beautiful analogies with elliptic curves and abelian varieties. They study of their moduli spaces leads amongst others to explicit class field theory, Jacquet-Langlands theory, and a proof of the Shimura-Taniyama-Weil conjecture for global function fields.This book constitutes a carefully written instructional course of 12 lectures on these subjects, including many recent novel insights and examples. The instructional part is complemented by research papers centering around class field theory, modular forms and Heegner points in the theory of global function fields.The book will be indispensable for everyone who wants a clear view of Drinfeld's original work, and wants to be informed about the present state of research in the theory of arithmetic geometry over function fields.
Book Synopsis Arithmetic Groups and Their Generalizations by : Lizhen Ji
Download or read book Arithmetic Groups and Their Generalizations written by Lizhen Ji and published by American Mathematical Soc.. This book was released on 2008 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as $\mathbf{Z}$ or $\textrm{SL}(n, \mathbf{Z})$. Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry. It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics. Titles in this series are co-published with International Press, Cambridge, MA.Table of Contents: Introduction; General comments on references; Examples of basic arithmetic groups; General arithmetic subgroups and locally symmetric spaces; Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups; Different completions of $\mathbb{Q}$ and $S$-arithmetic groups over number fields; Global fields and $S$-arithmetic groups over function fields; Finiteness properties of arithmetic and $S$-arithmetic groups; Symmetric spaces, Bruhat-Tits buildings and their arithmetic quotients; Compactifications of locally symmetric spaces; Rigidity of locally symmetric spaces; Automorphic forms and automorphic representations for general arithmetic groups; Cohomology of arithmetic groups; $K$-groups of rings of integers and $K$-groups of group rings; Locally homogeneous manifolds and period domains; Non-cofinite discrete groups, geometrically finite groups; Large scale geometry of discrete groups; Tree lattices; Hyperbolic groups; Mapping class groups and outer automorphism groups of free groups; Outer automorphism group of free groups and the outer spaces; References; Index. Review from Mathematical Reviews: ...the author deserves credit for having done the tremendous job of encompassing every aspect of arithmetic groups visible in today's mathematics in a systematic manner; the book should be an important guide for some time to come.(AMSIP/43.
