Non abelian 2-cohomology of semi-simple groups over rational varieties
Résumé
The aim of this paper is to study non abelian 2-cohomology of semi-simple groups over rational varieties. The essential invariant is the H 1 (k, Pic(¯ X)), where X is a rational variety over a p-adic field, or a number field, or more generally, a good field k of cohomological dimension 2. In particular, if ob(X) = 0 (ob(X) : elementary obstruction), we show that every class in H 2 (X, L), where L is an X-lien locally represented by a semi-simple simply connected group G, becomes neutral by the base change T c / / X / / X , where X is the Dynkin scheme of the associated G form G L to L, and T c a universal X-torsor compact-ification. This result confirms the fact that universal torsors compacti-fications have more simpler arithmetic.
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