Drinfeld Moduli Schemes And Automorphic Forms

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Drinfeld Moduli Schemes And Automorphic Forms

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Author : Yuval Z Flicker
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-04

Drinfeld Moduli Schemes And Automorphic Forms written by Yuval Z Flicker 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 2013-01-04 with Mathematics categories.

Drinfeld Moduli Schemes and Automorphic Forms: The Theory of Elliptic Modules with Applications is based on the author’s original work establishing the correspondence between ell-adic rank r Galois representations and automorphic representations of GL(r) over a function field, in the local case, and, in the global case, under a restriction at a single place. It develops Drinfeld’s theory of elliptic modules, their moduli schemes and covering schemes, the simple trace formula, the fixed point formula, as well as the congruence relations and a "simple" converse theorem, not yet published anywhere. This version, based on a recent course taught by the author at The Ohio State University, is updated with references to research that has extended and developed the original work. The use of the theory of elliptic modules in the present work makes it accessible to graduate students, and it will serve as a valuable resource to facilitate an entrance to this fascinating area of mathematics.

Drinfeld Modules Modular Schemes And Applications

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Author : M Van Der Put
language : en
Publisher: World Scientific
Release Date : 1997-08-27

Drinfeld Modules Modular Schemes And Applications written by M Van Der Put and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-27 with Mathematics categories.

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.

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.

Drinfeld Modular Forms Of Arbitrary Rank

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Author : Dirk Basson
language : en
Publisher: American Mathematical Society
Release Date : 2025-01-23

Drinfeld Modular Forms Of Arbitrary Rank written by Dirk Basson 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 2025-01-23 with Mathematics categories.

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Cohomology Of Drinfeld Modular Varieties Part 2 Automorphic Forms Trace Formulas And Langlands Correspondence

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Author :
language : en
Publisher: Cambridge University Press
Release Date :

Cohomology Of Drinfeld Modular Varieties Part 2 Automorphic Forms Trace Formulas And Langlands Correspondence written by 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 with categories.

Automorphic Forms And Shimura Varieties Of Pgsp 2

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Author : Yuval Z. Flicker
language : en
Publisher: World Scientific
Release Date : 2005

Automorphic Forms And Shimura Varieties Of Pgsp 2 written by Yuval Z. Flicker and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called OC liftings.OCO This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2, ?) in SL(4, ?). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum. Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations. To put these results in a general context, the book concludes with a technical introduction to LanglandsOCO program in the area of automorphic representations. It includes a proof of known cases of ArtinOCOs conjecture."

Automorphic Representations Of Low Rank Groups

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Author : Yuval Zvi Flicker
language : en
Publisher: World Scientific
Release Date : 2006

Automorphic Representations Of Low Rank Groups written by Yuval Zvi Flicker and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

The area of automorphic representations is a natural continuation of studies in number theory and modular forms. A guiding principle is a reciprocity law relating the infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called OC liftingsOCO. This book concentrates on two initial examples: the symmetric square lifting from SL(2) to PGL(3), reflecting the 3-dimensional representation of PGL(2) in SL(3); and basechange from the unitary group U(3, E/F) to GL(3, E), [E: F] = 2. The book develops the technique of comparison of twisted and stabilized trace formulae and considers the OC Fundamental LemmaOCO on orbital integrals of spherical functions. Comparison of trace formulae is simplified using OC regularOCO functions and the OC liftingOCO is stated and proved by means of character relations. This permits an intrinsic definition of partition of the automorphic representations of SL(2) into packets, and a definition of packets for U(3), a proof of multiplicity one theorem and rigidity theorem for SL(2) and for U(3), a determination of the self-contragredient representations of PGL(3) and those on GL(3, E) fixed by transpose-inverse-bar. In particular, the multiplicity one theorem is new and recent. There are applications to construction of Galois representations by explicit decomposition of the cohomology of Shimura varieties of U(3) using Deligne''s (proven) conjecture on the fixed point formula. Sample Chapter(s). Chapter 1: Functoriality and Norms (963 KB). Contents: On the Symmetric Square Lifting: Functoriality and Norms; Orbital Integrals; Twisted Trace Formula; Total Global Comparison; Applications of a Trace Formula; Computation of a Twisted Character; Automorphic Representations of the Unitary Group U(3, E/F): Local Theory; Trace Formula; Liftings and Packets; Zeta Functions of Shimura Varieties of U(3): Automorphic Representations; Local Terms; Real Representations; Galois Representations. Readership: Graduate students and researchers in number theory, algebra and representation theory."

The Arithmetic Of Function Fields

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Author : David Goss
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24

The Arithmetic Of Function Fields written by David Goss and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.

Thisseries is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.

Geometric Modular Forms And Elliptic Curves

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Author : Haruzo Hida
language : en
Publisher: World Scientific
Release Date : 2012

Geometric Modular Forms And Elliptic Curves written by Haruzo Hida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura?Taniyama conjecture, is given. In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction.In this new second edition, a detailed description of Barsotti?Tate groups (including formal Lie groups) is added to Chapter 1. As an application, a down-to-earth description of formal deformation theory of elliptic curves is incorporated at the end of Chapter 2 (in order to make the proof of regularity of the moduli of elliptic curve more conceptual), and in Chapter 4, though limited to ordinary cases, newly incorporated are Ribet's theorem of full image of modular p-adic Galois representation and its generalization to ?big? ?-adic Galois representations under mild assumptions (a new result of the author). Though some of the striking developments described above is out of the scope of this introductory book, the author gives a taste of present day research in the area of Number Theory at the very end of the book (giving a good account of modularity theory of abelian ?-varieties and ?-curves).

Arthur S Invariant Trace Formula And Comparison Of Inner Forms

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Author : Yuval Z. Flicker
language : en
Publisher: Birkhäuser
Release Date : 2016-09-14

Arthur S Invariant Trace Formula And Comparison Of Inner Forms written by Yuval Z. Flicker and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-14 with Mathematics categories.

This monograph provides an accessible and comprehensive introduction to James Arthur’s invariant trace formula, a crucial tool in the theory of automorphic representations. It synthesizes two decades of Arthur’s research and writing into one volume, treating a highly detailed and often difficult subject in a clearer and more uniform manner without sacrificing any technical details. The book begins with a brief overview of Arthur’s work and a proof of the correspondence between GL(n) and its inner forms in general. Subsequent chapters develop the invariant trace formula in a form fit for applications, starting with Arthur’s proof of the basic, non-invariant trace formula, followed by a study of the non-invariance of the terms in the basic trace formula, and, finally, an in-depth look at the development of the invariant formula. The final chapter illustrates the use of the formula by comparing it for G’ = GL(n) and its inner form G and for functions with matching orbital integrals.bribr/i/idiviiArthur’s Invariant Trace Formula and Comparison of Inner Forms/div