This volume is an English translation of "Cohomologie Galoisienne" . The original edition (Springer LN5, 1964) was based on the notes, written with the help of Michel Raynaud, of a course I gave at the College de France in 1962-1963. In the present edition there are numerous additions and one suppression: Verdier's text on the duality of profinite groups. The most important addition is the photographic reproduction of R. Steinberg's "Regular elements of semisimple algebraic groups", Publ. Math. LH.E.S., 1965. I am very grateful to him, and to LH.E.S., for having authorized this reproduction. Other additions include: - A proof of the Golod-Shafarevich inequality (Chap. I, App. 2). - The "resume de cours" of my 1991-1992 lectures at the College de France on Galois cohomology of k(T) (Chap. II, App.). - The "resume de cours" of my 1990-1991 lectures at the College de France on Galois cohomology of semisimple groups, and its relation with abelian cohomology, especially in dimension 3 (Chap. III, App. 2). The bibliography has been extended, open questions have been updated (as far as possible) and several exercises have been added. In order to facilitate references, the numbering of propositions, lemmas and theorems has been kept as in the original 1964 text. Jean-Pierre Serre Harvard, Fall 1996 Table of Contents Foreword ........................................................ V Chapter I. Cohomology of profinite groups §1. Profinite groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . .

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Authors and Affiliations

Collège de France, Paris, France

Jean-Pierre Serre

Bibliographic Information

Book Title: Galois Cohomology
Authors: Jean-Pierre Serre
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-642-59141-9
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1997
Hardcover ISBN: 978-3-540-42192-4Published: 23 October 2001
Softcover ISBN: 978-3-642-63866-4Published: 16 November 2012
eBook ISBN: 978-3-642-59141-9Published: 01 December 2013
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: X, 212
Additional Information: Originally published as a monograph
Topics: Algebra, Number Theory

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Table of contents (3 chapters)

Front Matter

Cohomology of profinite groups

Galois cohomology, the commutative case

Nonabelian Galois cohomology

Back Matter

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