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| Serre J. — Local Fields (Graduate Texts in Mathematics) |
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| Предметный указатель |
 field 161
Absolute ramification index 36
Absolutely unramified 36
Additive polynomial 90
Artin — Schreier (theory) 154—155
Artin, reciprocity law 24 221
Artin, representation 103 104 105
Artin, symbol 24
Artin, theorem of 99 102
Augmentation 114
Augmentation, ideal 127
Augmentation, representation 97
Brauer group 156
Brauer theorem 99
Central simple algebra 157
CHARACTER 97
Character, group 186
Class, formation 166
Class, function 97
Co-induced module 110
Cochain 112—114
Codifferent 50
Cohomologically trivial G-module 141
Cohomology of a group 111
Conductor of a character 103
Conductor of a ring 56
Conductor of an abelian extension 228
Corestriction 116 119 130
Crossed homomorphism 113
Cup-product 131—132
Decomposition group 21
Dedekind domain 10
Degree of a representation, or of its character 97
Different 50
Discrete valuation ring 5
Discriminant 49 50
Dwork theorem 200
Eisenstein polynomial 19
Existence theorem 173—175 218—220
Extension of the residue field 87
Extension of the residue field of groups 113
Factor set 113
Formation 165
Fractional ideal 11
Free generator 190
Frobenius substitution 23
Fuehrerdiskriminantenproduktformel 104
Fundamental class 196
G-homomorphism 109
G-module 109
Hasse — Arf theorem 76 93
Herbrand quotient 133
Herbrand theorem 75
Homology of a group 114
Induced character 98
Induced G-module 110
Induced representation 98
Inertia group 21
Inflation 116
Injective module 110
| Integral element 8
Integrally closed 8
Invertible ideal 9
Irreducible character 97
Jump 75
Kummer theory 155
Lattice 47
Linear representation 97
Local ring 7
Local symbols 204 206 214
Localisation 10
Maximal unramified extension 55
Multiplicative polynomial 90
Multiplicative system of representatives 35
Nakayama theorem 148—149
Noetherian ring 7
Norm group 172
Norm of an ideal 16
Norm residue symbol 197
Normalised absolute value 27
Order of an element 5
p-group 68 138
p-ring 37
Perfect ring 35
Prime ideal 5
Product formula 28
Projective module 110
Prolongation of a valuation 15
Quasi-algebraically closed field 161
Quasi-finite Fields 190
Ramification groups 62
Ramification index 14
Reciprocity, isomorphism 169 196
Reciprocity, law 24—25 222
Regular representation 97
Relatively injective (G-module) 110
Relatively projective (G-module) 110
Residue degree 14
Residue field 5
Restriction 116 119 129
Separable closure 54
Separable degree of a polynomial 90—91
Severi — Brauer variety 160
Shift operator Von Witt vectors 42
Split element ... by an extension 156
Strict p-ring 37—39
Sylow subgroup 139
Sylow theorem 139
Tate theorem 148—149
Topological G-module 154
Totally ramified extension 14
TRANSFER 120
Uniformizer 5
Unit of a ring 5
Unit representation 97
Unramified extension 14 53
Upper numbering of ramification groups 74
Valuation of an element 5
Witt polynomials 40
Witt vectors 42
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