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

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 \(H^1 (k,G) =0\).

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