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Drinfeld Moduli Schemes and Automorphic Forms

The Theory of Elliptic Modules with Applications

  • Book
  • © 2013

Overview

Authors:
  1. Yuval Z. Flicker

    1. , Department of Mathematics, The Ohio State University, Columbus, USA

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  • Provides a ?quick introduction to the Langlands correspondence for function fields via the cohomology of Drinfield moduli varieties
  • Complete exposition of the theory of elliptic modules, their moduli schemes and covering schemes, as well as new congruence relations and a "simple" converse theorem
  • Covers material that is known to experts and will be accesible to graduate students
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-v
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  2. Introduction

    • Yuval Z. Flicker
    Pages 1-8

  3. Elliptic Moduli

    1. Front Matter

      Pages 9-9
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  4. Elliptic moduli

    1. Elliptic Modules: Analytic Definition

      • Yuval Z. Flicker
      Pages 11-15

    2. Elliptic Modules: Algebraic Definition

      • Yuval Z. Flicker
      Pages 17-25

    3. Elliptic Modules: Geometric Definition

      • Yuval Z. Flicker
      Pages 27-36

    4. Covering Schemes

      • Yuval Z. Flicker
      Pages 37-42

  5. Hecke Correspondences

    1. Front Matter

      Pages 43-43
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  6. Hecke correspondences

    1. Deligne’s Conjecture and Congruence Relations

      • Yuval Z. Flicker
      Pages 45-63

  7. Trace Formulae

    1. Front Matter

      Pages 65-65
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  8. Trace formulae

    1. Isogeny Classes

      • Yuval Z. Flicker
      Pages 67-72

    2. Counting Points

      • Yuval Z. Flicker
      Pages 73-78

    3. Spherical Functions

      • Yuval Z. Flicker
      Pages 79-90

  9. Higher Reciprocity Laws

    1. Front Matter

      Pages 91-91
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    2. Purity Theorem

      • Yuval Z. Flicker
      Pages 93-103

    3. Existence Theorem

      • Yuval Z. Flicker
      Pages 105-111

    4. Representations of a Weil Group

      • Yuval Z. Flicker
      Pages 113-137

    5. Simple Converse Theorem

      • Yuval Z. Flicker
      Pages 139-148

  10. Back Matter

    Pages 149-154
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Keywords

About this book

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.

Authors and Affiliations

  • , Department of Mathematics, The Ohio State University, Columbus, USA

    Yuval Z. Flicker

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