Galois Groups over Q

TABLE OF CONTENTS
	PAGE

PREFACE                                           

G.	W. Anderson

NORMALIZATION or THE HYPERAD ELIC GAMMA FUNCTION	1
	l.	Gaussian units
	2.	The structure of	13
	3.	Normalization	23

D.	Blasius and D. Ramakrishnan
	MAASS FORMS AND GALOIS REPRESENTATIONS		33
		Automorphic forms via representations	37
	2.	Holomorphic automorphic forms for GSp(4)	40
		Geometric automorphic forms	44
	4.	Reductions	46
	5.	Heuristics and conjectures	49
	6.	Transfer of problem to GSp(4,P.Q)	54
		Hypothesis 1: structure of global L-packets for GSp(4)	57
	8.	An analytic estimate for the conjugates of Maass forms	59
	9.	hypothesis 2: Galois representations attached to Siegel
		    modular forms of higher weight	66
		The main theorem	68

P.	Deligne

LE GROUPE FONDAMENTAL DE LA DROITE PROJ ECTIVE MOINS
	TROIS POINTS
	0.	Terminologie et notations	87
		Motifs mixtes	89
	2.	Exemples
	3.	Torseurs sous Z(n)
	4.	Rappels sur les Ind-objets	127
	5.	Géométrie algébrique dans une catégorie tannakienne
		Le groupe fundamental d’une catégorie tannakienne
	7.	Géométrie algébrique dans Ia catégorie tannakienne des
		    systèmes de réalisations: interprétations	147
		Extensions itérées de motifs de Tate	163
	9.	Rappels sur les groupes unipotents	175
	10. Théories du
		   Groupoïdes
		   Tbéorie classique	183
		   Tbéorie profinie
	Tbéorie algébrique	193
		Le Frobenius cristallin du	de Rbam	204
	12.	La filtration de Hodge du		212
	13.	Le motivique
	14.	Exemple: le motivique	de	225
	15.	Points bases ~ l’infini		229
		  Théorie classique
		  Théorie profinie		237
		  Théorie algébrique		242
		  Compatibilités		246
		  Théorie motivique		252
	16.	  moins trois points: un quotient de	motivique	255
	17.	Relations de distribution: voie géométrique		270
	18.	Le torseur P, + est de torsion: voie géoméIrique
		Comparaison des Z(h)-torseurs des paragraphes 3 et 16		283
		Index des notations		293

Y.	Ihara
	THE GALOIS REPRESENTATION ARISINC FROM	{0,	AND
	TATE	TWISTS OF EVEN DECREE	299
	l.	Preliminaries and statement of the Theorem	300
	2.	Reducing the proof of the Theorem to two key lemmas	304
		Proof of Key Lemma A	307
	4.	Proof of Key Lemma B	309
	5.	Remarks and discussion	310
U.	Jannsen

ON THE -ADIC COHOMOLOGY OF VARIETIES OVER NUMBER FIELDS

AND ITS GALOIS COHOMOLOCY
		The basic conjecture
		Connections with algebraic K-theory	322
	3.	Connections with Iwasawa theory	329
	4.	Global results	335
	5.	The local case	341
	6.Thecasen≤i+l<2n		349
		The case i abelian varieties	353

B.	H. Matzat

RATIONALITY CRITERIA FOR GALOIS EXTENSIONS
	l.	Fundamental groups	363
	2.	Class numbers of generators	365
	3.	Topological automorphisms	369
	4.	Braids	374
		Braids and topological automorphisms together	378

B.	Mazur

DEFORMING GALOIS REPRESENTATIONS	385
	l. Universal deformation of representations	387
		   Deformations	387
		1.2 Existence of universal deformation rings	388
		1.3 Functoriality	392
		1.4 One-dimensional representations	396
		  The duality involution	398
		 1.6 Obstructions	398
		 1.7 Ordinary representations	400
		 1.8 Schur-type results
		 1.9 A few simple examples	403
		 1.10 Global Galois representations	404
		 1.11 Remarks on Galois representations to	406
		 1.12 Neat residual representations	407
		 1.13 Neat S3-extensions of Q	408
	2.	The internal structure of universal deformation spaces	411
		2.1 General glossary
		2.2 Special dihedral representations	414
	  The origin	415
	2.4 The globally dihedral locus	416

2.5	The ordinary locus
	2.6 The inertially reducible locus	422
	2.7 The inertially metabelian and the inertially dihedral locus . . .	425
	2.8 Loci of constant p-adic Hodge type	430

K.	Wingberg

GALOIS GROUPS OF POINCARÉ TYPE OVER ALGEBRAIC NUMBER
	FIELDS			(0.1
				in
		The function field case
				for
	   2.	Classification of Demukin groups	440

3.	p-adic number fields

4.	n-local fields

The absolute Galois group of a p-adic number field

6.	Global number fields

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