Class Field TheoryAmerican Mathematical Soc., 1968 - 192 pages This classic book, originally published in 1968, is based on notes of a year-long seminar the authors ran at Princeton University. The primary goal of the book was to give a rather complete presentation of algebraic aspects of global class field theory ... In this revised edition, two mathematical additions complementing the exposition of the original text are made. The new edition also contains several new footnotes, additional references, and historical comments. |
Table des matières
The First Fundamental Inequality | 11 |
Second Fundamental Inequality | 19 |
Sketch of the Analytic Proof of the Second Inequality | 33 |
The Existence Theorem | 52 |
Function Fields | 59 |
Connected Component of Idèle Classes | 65 |
The GrunwaldWang Theorem | 73 |
Higher Ramification Theory | 83 |
Explicit Reciprocity Laws | 109 |
Group Extensions | 127 |
Abstract Class Field Theory | 143 |
Weil Groups | 167 |
| 191 | |
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Expressions et termes fréquents
2-cocycle 2-dimensional abelian extension algebraic archimedean primes automorphism Axiom Brauer group Chapter character class field theory class formation cocycle class cohomology groups commutative compact consequently contains COROLLARY corresponding cyclic extension defined denote element exists extension of degree factor group finite index follows function fields fundamental class Galois group GF/GK GK/F global field group extension group G H²(G Hence homomorphism idèle classes induced integer invariant invp isomorphism K₁ kernel Kp/kp Lemma Let K/k norm residue symbol norm subgroup normal extension normal layer K/F number fields open subgroup prime degree prove ramified reciprocity law residue class field root of unity second inequality set of primes shows splits subfield subgroup of finite subgroup of G Theorem trivial UE/UE unramified V₁ Vi+1 W-diagram Weil group