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Zbl 0902.12004
Serre, Jean-Pierre
Galois cohomology. Transl. from the French by Patrick Ion. (English)
[B] Berlin: Springer. x, 210 pp. DM 78.00; öS 569.40; sFr. 69.00; \sterling 32.00; \$ 59.95 (1997). ISBN 3-540-61990-9/hbk

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 $H^1 (k,G) =0$.
[K.Hutchinson (Dublin)]

MSC 2000:: *12G05 Galois cohomology
12-02 Research monographs (field theory)
11-02 Research monographs (number theory)
11R34 Galois cohomology for global fields
11S25 Galois cohomology for local fields

Keywords: Galois cohomology; regular elements of semisimple algebraic groups

Citations: Zbl 0259.12011; Zbl 0174.08804; Zbl 0136.02801; Zbl 0136.30002

Cited in: Zbl 1225.12007 Zbl 1004.12003 Zbl 0909.20001

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