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INDEX

Adeles ........••...................... '" .

(th. fondamental) .

Approximation forte (th. d') .

Ca r a c t.e r-e .•••...•••••••••••••••.•.•...•.•.•••

Classe

d' ideaux .

de conjugaison modulo un groupe .

Classification (th. de)

local .

global .

Commutateurs .

Conducteur relatif d'un ordre .

Conjugaison •••...............................

Corestriction .....•..........................

Corps neutralisant .

Cycle .

Dedekind

(anneau de) .

(formule de nombre de classes) .

Dictionnaire qLobaLv-adeLi.que •••••••••••••••••

Differente .

Dirichlet

(formule analytique de nombre de classes)

(th. des unites) .

Discriminant

r edui.t. ..•••..•.....•••..•......•.••.•...

r edu i t, local .

local .

r edu i. t, global .

global .

Domaine fondamental

d'un s.-g. discret de SL(2,R) .

du groupe de Picard .................•...

pages

59

61

81

51,61,64,67

25,87,144

27,95-98

31

74

13

44

1

10,101

4,9,76-78

117

19

95

87

23

142

139

23

35,40

52

59,84

65

116,123

135

166

Eichler

(condi tion d' -) .

(th. des norme s ) .

(th. des progressions arithmetiques) .

(matrices d' )-Brandt .

Entier

(quaternion) .

(ideal) .. , ' ., .

Equations polynomiales en quaternions .

82

80,90

90

100,144

19

20

29

Fonction canonique

locale.............. . 52

globale. ... .. . ..... . . . .. . .. . . .. . . 67

Frobenius (th. de)........................... 7

Fujisaki (th. de)............................ 62

Genre de surfaces de Riemann................. 119

Graphe ari t.hrne t i.que . . . . . . . . . . . . . . . . . . . . . . . . . . 146

Groupes

finis de rotations...................... 14

finis de quaternions reels.............. 17

commensurables, arithmetiques, de quaternions 105

de picard............................... 108,135

modulaire de Hilbert

de congruence .

Hamilton (quaternions de) .

Hasse (invariant de) .

Hasse Minkowski (principe de) .

Homographie .

(multiplicateur, norme) .

primitive .

Hyperbolique (metrique) .

Ideal .

Ideles .

( th. fondamental) .

Isometrie

(cercle d') .

(groupe des) de .(groupe des) de ):13 .

107,109,120

4

32

75

111

115

128

112,133

20-22,86

59

62

111

112133

167

Leech (reseau de)............................ 149

Lobachevsky (fonction de).................... 134

Masse '" 141

Mesures

normalisees locales..................... 49

normalisees globales.................... 65

compatibles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Module d' un isomorphisme..................... 49

Niveau d'un ordre d'Eichler

local .

global '"

Normalisateur .•..............................

d'un ordre d'Eichler .

d'un groupe de congruence .

Norme

reduite d'un element .

reduite d'un ideal .

d 'un ideal •.............................

dans les ad eLe s .

Ordre .........•..............................

d 'Eichler local .......................•.

(arbre des) maximaux ................•...

euclidien , .

Place , .

Plongement maximal dans les ordres ..........•

(formules nurne r i que s ) .

Pointe ....................................•..

Po Lyriome minimal .•...........................

Produit

restreint .

tensoriel .

Quaternions sur (exemples)

(ordres, discriminants) .

(groupes de quaternions) ...............•

(e.E. n'est pas verifiee) .

39

84

29

39,99

121

1

24

47

60

19,20

39,55

40

90.156

57

23,36,42-44

92

117

2

59

9

79,85,98-99

108,120

143,161

168

Ramification

locale .

globale .

Regula':eur .

Representation (F-) de quaternions .

Re s e a u •••••••••••••••••••••••••••••••••••••••

(passage local-global) .

Residuel

(corps) .

(degre, extension) .

Riemann

31,35

58

138,139

4

19

83

34

35

(surface de) hyperelliptique............ 123

(surface)-ienne, isospectrale non isometrique 127

Schwartz-Bruhat (espace de)

local .

global .

Skolem-Noether (th. de) .

Symbole

de Hilbert .

d'Artin,d'Eichler .

Tamagawa

(mesure de) locale .

globale ' ' .

de SL(2,1R) •.••••.••••••••••

de SL(2,q:) •.•••••••.••••••.

(nombres de) .

Trace " .. ' .

r edu i t e ••....•.•.....•..••.••...•.....••

(formules de) .

Uni t.e s d' un ordre .

Uni formi sante .

Valuation .

va r i e t.e a.beLi.erme •.•••.••.•..•..••..••...••.•

Volumes (calculs de) .

Wedderburn (th. de) .

51

66

6

32,36,76

43,94,102

52

71

114

134

71

50

1

92-99,142

28,136

33

33

28

49,54,108-110,120

7

169

Zeta (fonction)

locale .

globale .

(formule mul tiplicative ) .

(Equation fonctionnelle) .

48,52

64

65,66

67