Local fields /
Serre, Jean Pierre, 1926-
Local fields / Jean-Pierre Serre ; translated from the French by Martin Jay Greenberg. - New York : Springer-Verlag, c1979. - viii, 241 p. ; 24 cm. - Graduate texts in mathematics ; 67 .
Includes index. Translation of Corps Locaux.
Bibliography: p. 232-237.
Contents: Basic results on discrete valuation rings, Dedekind domains, and completions.-Ramification theory: discriminant, different, ramification subgroups, Hasse-Arf theorem, Artin representations.-Group cohomology, with emphasis on arithmetical applications: theorems of Tate and Nakayama, Galois cohomology, class formations.-Local class field theory, presented from the cohomological point of view. The main result is the determination of the topological Galois group of the maximal abelian extension.
0387904247 3540904247 (Berlin)
Class field theory.
Homology theory.
QA247 / .S4613 1979
Local fields / Jean-Pierre Serre ; translated from the French by Martin Jay Greenberg. - New York : Springer-Verlag, c1979. - viii, 241 p. ; 24 cm. - Graduate texts in mathematics ; 67 .
Includes index. Translation of Corps Locaux.
Bibliography: p. 232-237.
Contents: Basic results on discrete valuation rings, Dedekind domains, and completions.-Ramification theory: discriminant, different, ramification subgroups, Hasse-Arf theorem, Artin representations.-Group cohomology, with emphasis on arithmetical applications: theorems of Tate and Nakayama, Galois cohomology, class formations.-Local class field theory, presented from the cohomological point of view. The main result is the determination of the topological Galois group of the maximal abelian extension.
0387904247 3540904247 (Berlin)
Class field theory.
Homology theory.
QA247 / .S4613 1979