Résumé des résultats (Abstract)
(Anglais)
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The objectives of this proposal are: To investigate problems in algebraic K-theory, linear algebraic groups, in particular, reductive groups, and their related structures like Azumaya algebras, Jordan algebras, Brauer groups, quadratic and Hermitean forms, by applying and combining methods from all these disciplines, in order to gain methadological synergy and to thereby considerably extend and stretch the range of the underlying theories.
This whole enterprise requires a coordinated cooperation of experts of all these distinct branches of mathematics, hence an expert network is the natural form of cooperation.
Due to recent progress in these fields already made, and due to the fact that the proposed network combines leading experts in all its areas, major breakthroughs can be expected in all fields covered by this network, in particular in algebraic K-theory, in the theory of anisotropic reductive groups, their internal structures, and their cohomological invariants, in the theories of Brauer groups, Azumaya and exceptional algebras, in quadratic and Hermitean forms and in many related areas like homotopy theory of schemes.
It is the main objective of this proposal to bring together the expertises of these fields in order to promote their research significantly by mutual benefit, and, in particular, to attract young researchers at the post doc level into this broad area by international exchange and intensive training.
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