Groupes algebriques semi-simples en dimension cohomologique 2: Semisimple algebraic groups in cohomological dimension 2

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La theorie des groupes algebriques sur un corps arbitraire est l'une des branches les plus merveilleuses des mathematiques modernes. Cette monographie porte sur les groupes algebriques semi-simples definis sur un corps k de dimension cohomologique separable 2 et la cohomologie galoisienne d'iceux. La question ouverte la plus importante est la conjecture II de Serre (1962) qui predit l'annulation de la cohomologie galoisienne d'un groupe semi-simple simplement connexe. Utilisant principalement des techniques de groupes algebriques, on couvre tous les cas connus de la conjecture: les cas classiques (dus a Bayer-Fluckiger and Parimala) ainsi que les avancees sur les cas exceptionnels restants (par exemple de type E8). Ceci s'applique a la classification des groupes semi-simples.

The theory of algebraic groups over arbitrary fields is one of the most beautiful branches of modern mathematics. This monograph deals with semisimple algebraic groups over a general field k of separable cohomological dimension ^ to Bayer-Fluckiger and Parimala), and some perspectives are given on the remaining exceptional cases (e.g., G of type E8). Applications to the classification of semisimple k-groups are presented.