Automorphic Forms, Shimura Varieties and L-Functions: Proceedings of a Conference Held at the University of Michigan, Ann Arbor, July 6-16, 1988 (Pe 9780121766528, 0121766527
288 87 9KB
English Pages 404 Year 1990
Table of contents :
Contents......Page 11
Blasius: Automorphic forms and Galois representations: some examples......Page 13
0 Introduction......Page 27
1 Definition of the local representations: the vanishing cycle side......Page 30
2 The rigid side......Page 34
3 Statement of the conjectures......Page 36
4 Proof of the conjectures for U... (sketch)......Page 40
5 The higher dimensional case......Page 48
Harris: Automorphic forms and the cohomology of vector bundles on Shimura varieties......Page 53
1 de Rham cohomology of local systems with growth conditions......Page 55
2 Automorphic forms as coherent cohomology classes......Page 63
3 dbar-cohomology of irreducible unitary representations; applications......Page 71
4 Faltings' (sic) B-G-G spectral sequence......Page 77
5 Rationality criteria for harmonic cusp forms......Page 83
6 Coherent cohomology defined by Eisenstein series......Page 88
7 Arithmetic applications......Page 93
References......Page 100
Hida: L-functions for base change lifts of GL2 and GL3......Page 105
1 p-adic modular forms of integral weight......Page 111
2 p-adic modular forms of half integral weight......Page 115
3 Eisenstein measure of half integral weight......Page 122
4 Arithmetic measures of half integral weight......Page 127
5 A special case of a quadratic form of one variable......Page 136
6 Primitive p-adic L-functions and proof of Theorem 1......Page 141
References......Page 153
1 Introduction......Page 155
2 Local combinatorics......Page 157
3 Mellin transforms......Page 165
4 Estimate for the Whittaker functions......Page 180
5 Global majorizations......Page 189
6 Global computations......Page 204
7 Local computations......Page 215
8 The global period integral......Page 225
9 The odd case......Page 227
References......Page 237
1 Preliminaries on motifs and L-functions......Page 239
2 Questions concerning Shimura varieties......Page 246
References......Page 258
Rapoport: On the bad reduction of Shimura varieties......Page 265
1 The geometry of the reduction in some examples......Page 267
2 The local factor of the Hasse-Weil zeta function......Page 273
3 Presentation of the examples......Page 283
Appendix to 3: the Drinfeld case......Page 298
4 Description of isogeny classes and their contribution to the semi-simple zeta function......Page 304
5 Comparison with the Selberg trace formula......Page 313
References......Page 331
Taylor: Representations of Galois groups associated to (sic) Hilbert modular forms......Page 335
Zink: The Lefschetz trace formula for an open algebraic surface......Page 349
1 Correspondences......Page 352
2 Deligne's conjecture......Page 356
3 The method of Neilsen-Wecken......Page 358
4 The Lefschetz formula for constant coefficients......Page 363
5 The lemma from commutative algebra......Page 379
6 Vanishing of the local terms......Page 382
References......Page 388
1 L2-cohomology and the statement of the conjecture......Page 389
2 Proof of the conjecture......Page 394
References......Page 401
Contents......Page 11
Blasius: Automorphic forms and Galois representations: some examples......Page 13
0 Introduction......Page 27
1 Definition of the local representations: the vanishing cycle side......Page 30
2 The rigid side......Page 34
3 Statement of the conjectures......Page 36
4 Proof of the conjectures for U... (sketch)......Page 40
5 The higher dimensional case......Page 48
Harris: Automorphic forms and the cohomology of vector bundles on Shimura varieties......Page 53
1 de Rham cohomology of local systems with growth conditions......Page 55
2 Automorphic forms as coherent cohomology classes......Page 63
3 dbar-cohomology of irreducible unitary representations; applications......Page 71
4 Faltings' (sic) B-G-G spectral sequence......Page 77
5 Rationality criteria for harmonic cusp forms......Page 83
6 Coherent cohomology defined by Eisenstein series......Page 88
7 Arithmetic applications......Page 93
References......Page 100
Hida: L-functions for base change lifts of GL2 and GL3......Page 105
1 p-adic modular forms of integral weight......Page 111
2 p-adic modular forms of half integral weight......Page 115
3 Eisenstein measure of half integral weight......Page 122
4 Arithmetic measures of half integral weight......Page 127
5 A special case of a quadratic form of one variable......Page 136
6 Primitive p-adic L-functions and proof of Theorem 1......Page 141
References......Page 153
1 Introduction......Page 155
2 Local combinatorics......Page 157
3 Mellin transforms......Page 165
4 Estimate for the Whittaker functions......Page 180
5 Global majorizations......Page 189
6 Global computations......Page 204
7 Local computations......Page 215
8 The global period integral......Page 225
9 The odd case......Page 227
References......Page 237
1 Preliminaries on motifs and L-functions......Page 239
2 Questions concerning Shimura varieties......Page 246
References......Page 258
Rapoport: On the bad reduction of Shimura varieties......Page 265
1 The geometry of the reduction in some examples......Page 267
2 The local factor of the Hasse-Weil zeta function......Page 273
3 Presentation of the examples......Page 283
Appendix to 3: the Drinfeld case......Page 298
4 Description of isogeny classes and their contribution to the semi-simple zeta function......Page 304
5 Comparison with the Selberg trace formula......Page 313
References......Page 331
Taylor: Representations of Galois groups associated to (sic) Hilbert modular forms......Page 335
Zink: The Lefschetz trace formula for an open algebraic surface......Page 349
1 Correspondences......Page 352
2 Deligne's conjecture......Page 356
3 The method of Neilsen-Wecken......Page 358
4 The Lefschetz formula for constant coefficients......Page 363
5 The lemma from commutative algebra......Page 379
6 Vanishing of the local terms......Page 382
References......Page 388
1 L2-cohomology and the statement of the conjecture......Page 389
2 Proof of the conjecture......Page 394
References......Page 401
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- Laurent Clozel
- James S. Milne
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