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Lecture Notes in Mathematics

By: Harry Reimann

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Paperback | 14 April 1997

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164 Pages

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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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Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Number Theory Geometry Algebraic Geometry

Introduction	p. 1
The basic embedding	p. 9
A reduction of Sh[subscript G]	p. 14
The local structure of [actual symbol not reproducible]	p. 22
Isogeny types of F-valued points	p. 30
The structure of an isogeny class	p. 38
A reduction of Sh[subscript D]	p. 47
Points on [actual symbol not reproducible] with values in finite fields	p. 59
The semi-simple local zeta function	p. 66
Orbital and twisted orbital integrals	p. 69
The trace formula	p. 78
Semi-simple automorphic L-functions	p. 83
A mysterious invariant of a CM-type	p. 89
Polarized abelian varieties over F	p. 93
The comparison of invariants	p. 99
Construction of algebraic groupoids	p. 106
The quasi-motivic groupoid	p. 114
The conjecture of Langlands and Rapoport	p. 127
References	p. 136
Symbol Index	p. 140
Subject Index	p. 143
Table of Contents provided by Blackwell. All Rights Reserved.

Lecture Notes in Mathematics

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