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Local fields / Jean-Pierre Serre.

By: Contributor(s): Material type: TextTextPublisher number: Variety Books Publishers | 2/22 Ansari Road, New Delhi-110002.Series: Graduate texts in mathematics, 67Publication details: New York : Springer-Verlag , ©1979.Description: 241 pages ; 24 cmISBN:
  • 9780387904245
Subject(s): Genre/Form:
DDC classification:
  • 512.74 SER
Contents:
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.
Summary: 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.
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Item type Current library Call number Status Barcode
Books Books SNU LIBRARY 512.74 SER (Browse shelf(Opens below)) Not For Loan 25446
Total holds: 0

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.

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