Article Dans Une Revue International Journal of Algebra and Computation Année : 2016

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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hal-01768666 , version 1 (19-04-2018)

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Bénaouda Djamai. Non abelian 2-cohomology of semi-simple groups over rational varieties. International Journal of Algebra and Computation, 2016, 10, pp.549 - 557. ⟨10.12988/ija.2016.61275⟩. ⟨hal-01768666⟩
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