The semi-simple zeta function of quaternionic Shimura varieties

  • Authors
  • Harry┬áReimann

Part of the Lecture Notes in Mathematics book series (LNM, volume 1657)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Harry Reimann
    Pages 1-8
  3. Harry Reimann
    Pages 9-65
  4. Harry Reimann
    Pages 66-88
  5. Back Matter
    Pages 89-144

About this book

Introduction

This monograph is concerned with the Shimura variety attached to a quaternion algebra over a totally real number field. For any place of good (or moderately bad) reduction, the corresponding (semi-simple) local zeta function is expressed in terms of (semi-simple) local L-functions attached to automorphic representations. In an appendix a conjecture of Langlands and Rapoport on the reduction of a Shimura variety in a very general case is restated in a slightly stronger form. The reader is expected to be familiar with the basic concepts of algebraic geometry, algebraic number theory and the theory of automorphic representation.

Keywords

algebra algebraic geometry algebraic number theory langlands program number theory shimura varieties zeta function

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0093995
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-62645-9
  • Online ISBN 978-3-540-68414-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book