Galois cohomology. Transl. from the French by Patrick Ion. (English) Zbl 0902.12004

Serre, Jean-Pierre

Berlin: Springer. x, 210 p. (1997).

This is a translation into English of the revised and completed fifth edition of Serre’s “Cohomologie Galoisienne”. It is a close and faithful translation and contains all of the added material of the latest edition.
This English edition also contains a photographic reproduction of the important paper, ‘Regular elements of semisimple algebraic groups’ [Inst. Hautes Étud. Sci., Publ. Math. 25, 281–312 (1965; Zbl 0136.30002)] by R. Steinberg, in which the following conjecture of Serre is proved: If \(k\) is a perfect field of cohomological dimension at most 1 and if \(G\) is a connected linear algebraic group defined over \(k\), then \(H^1 (k,G) =0\).

Reviewer: Kevin Hutchinson (Dublin)

MSC:

12G05	Galois cohomology
12-02	Research exposition (monographs, survey articles) pertaining to field theory
11-02	Research exposition (monographs, survey articles) pertaining to number theory
11R34	Galois cohomology
11S25	Galois cohomology

Keywords:

Galois cohomology; regular elements of semisimple algebraic groups

Citations:

Zbl 0259.12011; Zbl 0174.08804; Zbl 0136.02801; Zbl 0136.30002