The semi-simple zeta function of quaternionic Shimura varieties

Harry Reimann (auth.)354062645X, 9783540626459

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.

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Table of contents :
Introduction….Pages 1-8
Part I….Pages 9-65
Part II….Pages 66-88