La th???orie des groupes alg???briques sur un corps arbitraire est l'une des branches les plus merveilleuses des math???matiques modernes. Cette monographie porte sur les groupes alg???briques semi-simples d???finis sur un corps k de dimension cohomologique s???parable Utilisant principalement des techniques de groupes alg???briques, on couvre tous les cas connus de la conjecture: les cas classiques (dus ??? Bayer-Fluckiger and Parimala) ainsi que les avanc???es sur les cas exceptionnels restants (par exemple de type E8). ...
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La th???orie des groupes alg???briques sur un corps arbitraire est l'une des branches les plus merveilleuses des math???matiques modernes. Cette monographie porte sur les groupes alg???briques semi-simples d???finis sur un corps k de dimension cohomologique s???parable Utilisant principalement des techniques de groupes alg???briques, on couvre tous les cas connus de la conjecture: les cas classiques (dus ??? Bayer-Fluckiger and Parimala) ainsi que les avanc???es sur les cas exceptionnels restants (par exemple de type E8). Ceci s'applique ??? 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.
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