Local Fields

This article has multiple issues. Please help or discuss these issues on the talk page. (Learn how and when to remove these template messages) This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help by introducing citations to additional sources. Find sources:  –  ·  ·  · scholar · JSTOR (November 2020) This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. Please help to improve this article by introducing more precise citations. (November 2020) (Learn how and when to remove this template message) (Learn how and when to remove this template message)

Local Fields

Author	Jean-Pierre Serre
Original title	Corps Locaux
Country	France
Language	French (original) English (translation)
Subject	Algebraic Number Theory
Genre	Non-fiction
Publisher	Springer
Publication date	1980
Media type	Print
Pages	241 pp.
ISBN	978-0-387-90424-5
OCLC	4933106

Corps Locaux by Jean-Pierre Serre, originally published in 1962 and translated into English as Local Fields by Marvin Jay Greenberg in 1979, is a seminal graduate-level algebraic number theory text covering local fields, ramification, group cohomology, and local class field theory. The book's end goal is to present local class field theory from the cohomological point of view. This theory concerns extensions of "local" (i.e., complete for a discrete valuation) fields with finite residue field.^{[dubious – discuss]}

Contents[]

1. Part I, Local Fields (Basic Facts): Discrete valuation rings, Dedekind domains, and Completion.
2. Part II, Ramification: Discriminant & Different, Ramification Groups, The Norm, and Artin Representation.
3. Part III, Group Cohomology: Abelian & Nonabelian Cohomology, Cohomology of Finite Groups, Theorems of Tate and Nakayama, Galois Cohomology, Class Formations, and Computation of Cup Products.
4. Part IV, Local Class Field Theory: Brauer Group of a Local Field, Local Class Field Theory, Local Symbols and Existence Theorem, and Ramification.

References[]

• Serre, Jean-Pierre (1980), Local Fields, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90424-5, MR 0554237

This article about a mathematical publication is a stub. You can help Wikipedia by .

• v
• t