Jean-Pierre Serre. creator Jean-Pierre Serre. text Homology theory.-Algebra xxu New York : Springer-Verlag , ©1979 monographic eng

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241 pages ; 24 cm. 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. 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. / Jean-Pierre Serre. Mathematics 512.74 SER 9780387904245 Variety Books Publishers 2/22 Ansari Road, New Delhi-110002. 180727 20180727161036.0