Neukirch J. — Class Field Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Neukirch J. — Class Field Theory

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Название: Class Field Theory

Автор: Neukirch J.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 140

Добавлена в каталог: 01.06.2008

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Предметный указатель

"Hilbert 90"      14
$\mathbb{Z}_{p}$ -extension, cyclotomic      92
$\widehat{\mathbb{Z}}$       6
$\widehat{\mathbb{Z}}$ -extension      19 91
$\widehat{\mathbb{Z}}$ -extension, cyclotomic      92
Abscissa of convergence      114
Absolute Galois group      1
Absolute value      37 72
Adeles      76
Artin conductor      126
Artin conjecture      126
Artin L-series      123
Artin symbol      105 128
Birch and Swinnerton-Dyer, conjecture of      119
CHARACTER      120 122
Character, principal      122
Class field axiom      28 37 39
Class field axiom, global      89
Class field axiom, local      39
Class field theory      18 28
Class field theory over $\mathbb{R}$       43
Class field theory, general      18 28
Class field theory, global      72 94
Class field theory, local      37 43
Class field tower problem      110
Class fields      30 31
Class fields, global      96
Class fields, Hilbert      99
Class fields, local      43 63
Class fields, ray      99
Class number      72
Class number formula      119
Cocycle      9
Conductor      44 99 126
Congruence subgroup      98
Critical strip      117
Crossed homomorphism      9
CYCLE      97 120 128
Cycle of declaration      103 104
Cyclotomic extensions      46
Decomposition group      74
Decomposition law of primes      106
Deg      18
Density, "probabilistic", "natural"      130
Density, Dirichlet      130
Directed set      4
Dirichlet density theorem      131
Dirichlet L-series      120
Dirichlet prime number theorem      129
Dirichlet series      113
Dirichlet's unit theorem      72
Division points      61
Double cosets      26
Equidistribution      132
Euler identity      115 118
Existence theorem, global      97
Existence theorem, local      44
exp, p-adic      38
Fixed module      8
Formal $\mathcal{O}$ -module      57
Formal $\mathcal{O}$ -module, homomorphism of      57
Formal group      56
Formal group, additive      56
Formal group, multiplicative      56 57
Frobenius      19
Frobenius automorphism      1 7 41
Frobenius endomorphism      57
Frobenius lift      20
Functional equation      116 119 121 127
G-homomorphism      8
G-module      8
G-module, induced      10 83
G-module, trivial      8
Gamma function      116
Group, procyclic      6
Group, profinite      4
Hasse norm theorem      89
Hasse — Arf,theorem of      68
Henselian valuation      20 93
Herbrand quotient      12
Herbrand quotient, multiplicativity of      13
Hexagon, exact      12
Hilbert class field      99 107
Hilbert symbol      50
Hilbert symbol, explicit      54 55
Hilbert symbol, tame      52 53
Ideal class group      72 78
Idele class group      77
Idele group      77
Ideles      76 77

Ideles, principal      77
Inertia degree      19 33
Inertia group      64
Infinite extensions      32
Infinite Galois theory      1
Infinite galois theory, main theorem of      3
Iwasawa theory      119
Kronecker — Weber, theorem of      45 46 64
Krull topology      2
Kummer extension      15 86
Kummer theory      14 15
L-series      120
L-series, Artin      123
L-series, Dirichlet      120
Langlands Philosophy      129 135
Lattice      73 74
Legendre symbol      53
Leopoldt Conjecture      102
Local components of ideles      77 82
Local field      7 37
log, p-adic      38
Lubin — Tate extension      62 65
Lubin — Tate module      57
Lubin — Tate polynomial      48
Maximal abelian p-extension      100
Norm      9 82
Norm group      9
Norm residue group      9 85
Norm residue symbol      29
Norm residue symbol over $\mathbb{Q}_{p}$       46
Norm residue symbol over $\mathbb{R}$       43
Norm residue symbol, explicit      49
Norm residue symbol, global      94
Norm residue symbol, local      42
Norm theorem, Hasse      89
Norm topology      31
p-adic integers      6
p-adic number field      37
p-adic unit rank      102
Pontrjagin dual      7
Power residue symbol      53 110 111
Prime      72
Prime decomposition law      106
Prime element      21 37
Prime, complex      72
Prime, finite      72
Prime, infinite      72
Prime, real      72
Principal ideal theorem      107
Procyclic group      6
Product formula of absolute values      72
Product formula of norm residue symbols      95
Profinite completion      8
Profinite group      4
Projective limit      4
Projective system      4
Pruefer ring      6
Ramification groups      64
Ramification groups, jumps of      68
Ramification groups, upper numbering of      67
Ray      103
Ray class field      99
Ray class group      98 103
Reciprocity law of n-th power residues      111
Reciprocity law, Artin's global      94
Reciprocity law, Gauss      112
Reciprocity law, general      28
Reciprocity law, local      42
Reciprocity map      22
Representation      122
Riemann hypothesis      117
S-ideles      77
S-units      72
Symbol      105
Symbol, Artin      105
Symbol, Hilbert      50
Symbol, norm residue      29 42 43 46 49 94
Tchebotarev's density theorem      132
Trace      9
UNITS      37
Units, principal      37
Universal norms      31
Valuation      37
Valuation ring      37
Verlagerung      26
Weil group      69
Zeta function, Dedekind      117
Zeta function, Leopoldt      119
Zeta function, partial      118
Zeta function, Riemann      113

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