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Galois cohomology. Transl. from the French by Patrick Ion. (English) Zbl 0902.12004
Berlin: Springer. x, 210 pp. DM 78.00; öS 569.40; sFr. 69.00; £ 32.00; $ 59.95 (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 Etud. Sci., Publ. Math. 25, 281-312 (1965; Zbl 0136.30002)] by {\it 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 $H^1 (k,G) =0$.

12G05Galois cohomology
12-02Research monographs (field theory)
11-02Research monographs (number theory)
11R34Galois cohomology for global fields
11S25Galois cohomology for local fields