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Drinfeld Moduli Schemes and Automorphic Forms

The Theory of Elliptic Modules with Applications

  • Yuval Z. Flicker

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-v
  2. Yuval Z. Flicker
    Pages 1-8
  3. Elliptic Moduli

    1. Front Matter
      Pages 9-9
    2. Yuval Z. Flicker
      Pages 11-15
    3. Yuval Z. Flicker
      Pages 17-25
    4. Yuval Z. Flicker
      Pages 27-36
    5. Yuval Z. Flicker
      Pages 37-42
  4. Hecke Correspondences

    1. Front Matter
      Pages 43-43
  5. Trace Formulae

    1. Front Matter
      Pages 65-65
    2. Yuval Z. Flicker
      Pages 67-72
    3. Yuval Z. Flicker
      Pages 73-78
    4. Yuval Z. Flicker
      Pages 79-90
  6. Higher Reciprocity Laws

    1. Front Matter
      Pages 91-91
    2. Yuval Z. Flicker
      Pages 93-103
    3. Yuval Z. Flicker
      Pages 105-111
    4. Yuval Z. Flicker
      Pages 113-137
    5. Yuval Z. Flicker
      Pages 139-148
  7. Back Matter
    Pages 149-154

About this book

Introduction

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.

Keywords

Drinfield modules Galois representations Ramanujan conjecture cuspidal representations elliptic modules function fields

Authors and affiliations

  • Yuval Z. Flicker
    • 1
  1. 1., Department of MathematicsThe Ohio State UniversityColumbusUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-5888-3
  • Copyright Information Yuval Z. Flicker 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-5887-6
  • Online ISBN 978-1-4614-5888-3
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site
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