The Trace Formula and Base Change for GL (3)
- PDF / 8,786,197 Bytes
- 217 Pages / 461 x 684 pts Page_size
- 37 Downloads / 272 Views
927 Yuval Z. Flicker
The Trace Formula and Base Change for GL(3)
Springer-Verlag Berlin Heidelberg New York 1982
Author
Yuval Z. Flicker Department of Mathematics, Princeton University Fine Hall - Box 37, Princeton NJ 08544, USA
AMS Subject Classifications (1980): 10040, 12A85, 22E50, 22E55 ISBN 3-540-11500-5 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-11500-5 Springer-Verlag New York Heidelberg Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1982 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
Table of Contents Introduction 1.
2.
vi
LOCAL THEORY 1.1.1. 1.1.2. 1.1. 3. 1.1.4.
Notations The norm map Local v , global Galois cohomology
1.2.1. 1.2.2. 1.2.3. 1.2.4. 1.2.5. 1.2.6.
G(F)-families Twisted G(F)-families Matching orbital integrals End of proof Reformulation Spherical functions
9 12 13
1. 3.1. 1.3.2. 1.3.3. 1.3.4. 1.4.1. 1.4.2. 1.4.3.
Classification Twisted characters Induced representations Local lifting
24 26 27 31
Orthogonality relations Supercuspidals Twisted orthogonality relations
34 36
38
1.5.1. 1.5.2. 1. 5. 3. 1. 5.4. 1. 5.5.
Split places Matching functions Lifting representations Weighted integrals Matching operators
41 42 43 45 46
1
2
5
6
18 20
22
THE TRACE FORMULA 2.1.1. 2.1.2. 2.1.3.
Introduction Measures The map H
2.2.1. 2.2.2. 2.2.3.
The distribution Elliptic terms Quadratic terms
49 51 52
J
o
54 56 57
2.3.1. Correction for GL(2) 2.3.2. The correction 2.3.3. Singular classes 2.3.4. The term LoIo(f) 2.4.1.-2.4.4. Proof of Lemma 3 2.5.1.-2.5.6. Proof of Lemma 4 2.6.1.-2.6.3. Integration lemma
78 88
2.7.1. 2.7.2. 2.7.3.
96 98
Asymptotic behavior At h = 1 Division algebras
59 63
66 68 71
95
IV
3.
4.
THE TWISTED TRACE FORMULA 3.1.1. 3.1.2. 3.1.3. 3.1.4.
Introduction The twisted distribution Elliptic terms Quadrati c terms
3.2.1. 3.2.2. 3.2.3. 3.2.4.
Twisted correction for GL(2,E) Twisted correction for GL(3,E) Singular twisted classes The term I ( 4) )
100 102 103 104 109 112 116 118
3.3.1. 3.3.2.
Proof of Lemma 7 Final contribution
121 124
3.4.1. 3.4.2.
Asymptotic behavior for Asymptotic behavior for
Lo
o
o
GL(2,E) GL(3,E)
125 127
THE CONTINUOUS SPECTRUM 4.1.I. 4.1.2. 4.2.I.
Notations Kernels The Ix(f) and 4.2.1. (a) 'PX = {G} 4.2.1.(b) 4.2.I.(c)
4.2.1.(c) 4.2.I.(c)
5.
J
= {PI} Px = {PO} , Px = {PO} , Px
Px = {PO}
,
I (4)) X
129 131 135 135 136
A'
= AO
A' = Al A' = Z
138 139 142
4.2.2.
Reformulation
143
4.3.1. 4.3.2. 4.3.3.
The Hecke algebra The discrete series A sum
147 149 ::.51
EQUALITY OF TRACES 5.1.I. 5.1.2. 5.1.3. 5.1.4.
Eliptic te
Data Loading...
