Cohomology Of Drinfeld Modular Varieties Part 1 Geometry Counting Of Points And Local Harmonic Analysis
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Cohomology Of Drinfeld Modular Varieties Part 1 Geometry Counting Of Points And Local Harmonic Analysis
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Author : Gérard Laumon
language : en
Publisher: Cambridge University Press
Release Date : 1996
Cohomology Of Drinfeld Modular Varieties Part 1 Geometry Counting Of Points And Local Harmonic Analysis written by Gérard Laumon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
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.
Cohomology Of Drinfeld Modular Varieties Part 1 Geometry Counting Of Points And Local Harmonic Analysis
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Author : Gérard Laumon
language : en
Publisher: Cambridge University Press
Release Date : 2010-12-09
Cohomology Of Drinfeld Modular Varieties Part 1 Geometry Counting Of Points And Local Harmonic Analysis written by Gérard Laumon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-09 with Mathematics categories.
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.
Cohomology Of Drinfeld Modular Varieties Geometry Counting Of Points And Local Harmonic Analysis
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Author : Gérard Laumon
language : en
Publisher:
Release Date : 1996
Cohomology Of Drinfeld Modular Varieties Geometry Counting Of Points And Local Harmonic Analysis written by Gérard Laumon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Drinfeld modular varieties categories.
Weil Conjectures Perverse Sheaves And L Adic Fourier Transform
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Author : Reinhardt Kiehl
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Weil Conjectures Perverse Sheaves And L Adic Fourier Transform written by Reinhardt Kiehl 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 2013-03-14 with Mathematics categories.
In this book the authors describe the important generalization of the original Weil conjectures, as given by P. Deligne in his fundamental paper "La conjecture de Weil II". The authors follow the important and beautiful methods of Laumon and Brylinski which lead to a simplification of Deligne's theory. Deligne's work is closely related to the sheaf theoretic theory of perverse sheaves. In this framework Deligne's results on global weights and his notion of purity of complexes obtain a satisfactory and final form. Therefore the authors include the complete theory of middle perverse sheaves. In this part, the l-adic Fourier transform is introduced as a technique providing natural and simple proofs. To round things off, there are three chapters with significant applications of these theories.
Recent Progress In Algebra
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Author : Sang Geun Hahn
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Recent Progress In Algebra written by Sang Geun Hahn 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 1999 with Mathematics categories.
This volume presents the proceedings of the international conference on "Recent Progress in Algebra" that was held at the Korea Advanced Institute of Science and Technology (KAIST) and Korea Institute for Advanced Study (KIAS). It brought together experts in the field to discuss progress in algebra, combinatorics, algebraic geometry and number theory. This book contains selected papers contributed by conference participants. The papers cover a wide range of topics and reflect the current state of research in modern algebra.
Arithmetic Quotients Of The Bruhat Tits Building For Projective General Linear Groups In Positive Characteristic
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Author : Satoshi Kondo
language : en
Publisher: American Mathematical Society
Release Date : 2025-02-25
Arithmetic Quotients Of The Bruhat Tits Building For Projective General Linear Groups In Positive Characteristic written by Satoshi Kondo and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-25 with Mathematics categories.
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Arithmetic Geometry Cryptography And Coding Theory 2021
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Author : Samuele Anni
language : en
Publisher: American Mathematical Society
Release Date : 2022-07-06
Arithmetic Geometry Cryptography And Coding Theory 2021 written by Samuele Anni and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-06 with Mathematics categories.
This volume contains the proceedings of the 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, held (online) from May 31 to June 4, 2021. For over thirty years, the biennial international conference AGC$^2$T (Arithmetic, Geometry, Cryptography, and Coding Theory) has brought researchers together to forge connections between arithmetic geometry and its applications to coding theory and to cryptography. The papers illustrate the fruitful interaction between abstract theory and explicit computations, covering a large range of topics, including Belyi maps, Galois representations attached to elliptic curves, reconstruction of curves from their Jacobians, isogeny graphs of abelian varieties, hypergeometric equations, and Drinfeld modules.
Arithmetic And Geometry
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Author : Luis Dieulefait
language : en
Publisher: Cambridge University Press
Release Date : 2015-10-08
Arithmetic And Geometry written by Luis Dieulefait and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-08 with Mathematics categories.
The world's leading authorities describe the state of the art in Serre's conjecture and rational points on algebraic varieties.
Drinfeld Modules
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Author : Mihran Papikian
language : en
Publisher: Springer Nature
Release Date : 2023-03-31
Drinfeld Modules written by Mihran Papikian and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-31 with Mathematics categories.
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.
Arithmetic Groups And Their Generalizations
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Author : Lizhen Ji
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Arithmetic Groups And Their Generalizations written by Lizhen Ji 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 2008 with Mathematics categories.
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.