By Mikhail Borovoi

During this quantity, a brand new functor $H^2_{ab}(K,G)$ of abelian Galois cohomology is brought from the class of attached reductive teams $G$ over a box $K$ of attribute $0$ to the class of abelian teams. The abelian Galois cohomology and the abelianization map$ab^1:H^1(K,G) \rightarrow H^2_{ab}(K,G)$ are used to provide a functorial, nearly particular description of the standard Galois cohomology set $H^1(K,G)$ whilst $K$ is a bunch box.

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Kn3] M. Kneser, Lectures on Galois Cohomology of Classical Groups, Tata Institute of Fundamental Research Lectures on Mathematics 47, Bombay 1969. [Ko1] R. E. Kottwitz, Rational conjugacy classes in reductive groups, Duke Math. J. 49 (1982), 785–806. [Ko2] R. E. Kottwitz, Stable trace formula: cuspidal tempered terms, Duke Math. J. 51 (1984), 611–650. [Ko3] R. E. Ann. 275 (1986), 365–399. [La1] R. P. Langlands, On the classification of irreducible representations of real algebraic groups, Representation Theory and Harmonic Analysis on Semisimple Lie Groups, Mathematical Surveys and Monographs, vol.

Grothendieck, SGA1. Revˆetements ´etale et group fondamental, Lecture Notes in Math. 224, Springer, Berlin, 1971. [Ha1] ¨ G. Harder, Uber die Galoiskohomologie halbeinfacher Matrizengruppen. I, Math. Zeit. 90 (1965), 404–428; II, Math. Zeit 92 (1966), 396–415. [Ha2] G. Harder, Bericht u ¨ber neuere Resultate der Galoiskohomologie halbeinfacher Matrizengruppen, Jahresbericht d. DMV 70 (1968), 182–216. [Kn1] M. Kneser, Galoiskohomologie halbeinfacher algebraischer Gruppen u ¨ber p-adi schen K¨ orpern.

Kn2] M. Kneser, Hasse principle for H 1 of simply connected groups, Algebraic Groups and Discontinuous Subgroups, Proc. Sympos. Pure Math. 9, AMS, Providence, RI, 1966, pp. 159–163. [Kn3] M. Kneser, Lectures on Galois Cohomology of Classical Groups, Tata Institute of Fundamental Research Lectures on Mathematics 47, Bombay 1969. [Ko1] R. E. Kottwitz, Rational conjugacy classes in reductive groups, Duke Math. J. 49 (1982), 785–806. [Ko2] R. E. Kottwitz, Stable trace formula: cuspidal tempered terms, Duke Math.