01497nam a22002297a 4500 20180727161036.0 180727b xxu||||| |||| 00| 0 eng d 9780387904245 Variety Books Publishers 2/22 Ansari Road, New Delhi-110002. 512.74 SER 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. Mathematics Homology theory. Algebra Jean-Pierre Serre. BOOK 50011 50011 0 0 ddc 0 1 SNUL SNUL 2018-07-27 0 512.74 SER 25446 2018-07-27 00:00:00 2018-07-27 BOOK