Serre J. — Local Fields (Graduate Texts in Mathematics 67) :: Электронная библиотека попечительского совета мехмата МГУ

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Serre J. — Local Fields (Graduate Texts in Mathematics 67)

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Название: Local Fields (Graduate Texts in Mathematics 67)

Автор: Serre J.

Аннотация:

This is a translation of Corps Locaux, supplemented with an updated bibliography and some new exercises. This book is accessible to graduate students, and can be used as a reference source by research mathematicians in algebra and number theory.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1979

Количество страниц: 252

Добавлена в каталог: 16.12.2014

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Предметный указатель

$C_{1}$ field      161
Absolute ramification index      36
Absolutely unramified      36
Additive polynomial      90
Artin reciprocity law      24 221
Artin representation      103 104 105
Artin symbol      24
Artin — Schreier (theory)      154—155
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 groups      113
Extension of the residue field      87
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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