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 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.

Proceedings Of The Workshop On Drinfeld Modules Modular Schemes And Applications

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Author : Ernst-Ulrich Gekeler
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 1997

Proceedings Of The Workshop On Drinfeld Modules Modular Schemes And Applications written by Ernst-Ulrich Gekeler and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

Drinfeld Modular Curves

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Author : Ernst-Ulrich Gekeler
language : en
Publisher: Springer
Release Date : 2006-11-14

Drinfeld Modular Curves written by Ernst-Ulrich Gekeler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Compactification Of The Drinfeld Modular Surfaces

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Author : Thomas Lehmkuhl
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-01-21

Compactification Of The Drinfeld Modular Surfaces written by Thomas Lehmkuhl 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 2009-01-21 with Science categories.

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.

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

Automorphic Forms And Shimura Varieties Of Pgsp 2

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

Automorphic Forms And Shimura Varieties Of Pgsp 2 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 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 ?liftings.' 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,ó) in SL(4, ó). 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 Langlands' program in the area of automorphic representations. It includes a proof of known cases of Artin's conjecture.

Elliptic Curves Modular Forms And Iwasawa Theory

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Author : David Loeffler
language : en
Publisher: Springer
Release Date : 2017-01-15

Elliptic Curves Modular Forms And Iwasawa Theory written by David Loeffler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-15 with Mathematics categories.

Celebrating one of the leading figures in contemporary number theory – John H. Coates – on the occasion of his 70th birthday, this collection of contributions covers a range of topics in number theory, concentrating on the arithmetic of elliptic curves, modular forms, and Galois representations. Several of the contributions in this volume were presented at the conference Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John Coates in Cambridge, March 25-27, 2015. The main unifying theme is Iwasawa theory, a field that John Coates himself has done much to create. This collection is indispensable reading for researchers in Iwasawa theory, and is interesting and valuable for those in many related fields.

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 Political Science 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 ?liftings?. 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 ?Fundamental Lemma? on orbital integrals of spherical functions. Comparison of trace formulae is simplified using ?regular? functions and the ?lifting? 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.