Cohomologies orientées équivariantes, variétés de drapeaux et motifs

Contact: Anne Quéguiner-Mathieu.

Kirill Zainoulline donnera une série de trois exposés sur les cohomologies orientées équivariantes, les variétés de drapeaux et les motifs. * le premier à Paris 13, mercredi 18 mai à 13h45, en B405; * le deuxième et le troisième à l'IHP, lundi 23 et mardi 24 mai à 14h en salle 421.

Résumé:

Given an equivariant oriented cohomology theory h, a split semisimple linear algebraic group G over a field k, a maximal torus T in G, and a parabolic subgroup P containing T, we explain how the T-equivariant oriented cohomology ring hT(G/P) can be identified with the dual of a coalgebra defined using exclusively the root datum of (G,T), a set of simple roots defining P and the formal group law of h. Our main tool is the pull-back to the T-fixed points of G/P which injects the cohomology ring in question into a direct product of a finite number of copies of the T-equivariant oriented cohomology of a point. Let E be a G-torsor over k. Consider a twisted form E/B of the variety of Borel subgroups G/B. As an application of our techniques, we establish an equivalence between the h-motivic subcategory generated by E/B and the category of projective modules for certain Hecke-type algebra which depends on the root system of G, its isogeny class, on E, and on the formal group law of the theory h.