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Jean-Pierre Serre.

Local fields / Jean-Pierre Serre. - New York : Springer-Verlag , ©1979. - 241 pages ; 24 cm. - Graduate texts in mathematics, 67. .

pt. I. Local fields (basic facts). Discrete valuation rings and Dedekind domains --
Completion --
pt. II. Ramification. Discriminant and different --
Ramification groups --
The norm --
Artin representation --
pt. III. Group cohomology. Basic facts --
Cohomology of finite groups --
Theorems of Tate and Nakayama --
Galois cohomology --
Class formations --
pt. IV. Local class field theory. Brauer groups of a local field ---
Local class field theory --
Local symbols and existence theorem --
Ramification.

The goal of this book is to present local class field theory from the cohomo- logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field.

ISBN: 9780387904245

Publisher. No.: Variety Books Publishers 2/22 Ansari Road, New Delhi-110002.

Subjects--Topical Terms:
Mathematics

Index Terms--Genre/Form: --Homology theory.--Algebra

Dewey Class. No.: 512.74 SER