Local Fields

Local Fields

This article has multiple issues. Please help improve it 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 improve this articlebyintroducing citations to additional sources.
Find sources: "Local Fields" – news · newspapers · books · 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 improve this article by introducing more precise citations. (November 2020) (Learn how and when to remove this message)

(Learn how and when to remove this message)

Corps LocauxbyJean-Pierre Serre, originally published in 1962 and translated into English as Local FieldsbyMarvin 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]}

Local Fields

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

Local Fields

Author

Jean-Pierre Serre

Original title

Corps Locaux

Language

French (original)
English (translation)

Subject

Algebraic number theory

Genre

Non-fiction

Publisher

Springer

Publication date

1980

Publication place

France

Media type

Pages

241 pp.

Part I, Local Fields (Basic Facts): Discrete valuation rings, Dedekind domains, and Completion.
Part II, Ramification: Discriminant & Different, Ramification Groups, The Norm, and Artin Representation.
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.
Part IV, Local Class Field Theory: Brauer Group of a Local Field, Local Class Field Theory, Local Symbols and Existence Theorem, and Ramification.

References

Last edited on 20 December 2023,

at 22:48

Languages

This page is not available in other languages.

●This page was last edited on 20

December 2023, at 22:48 (UTC).

●Content is available under CC B

Y-SA 4.0 unless otherwise noted.

Contents

References

Languages