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Variétés rationnelles

Horaires : Le vendredi 11 mars 2016, 16h30-17h30

Lieu : ENS, 29 rue d'Ulm, salle 236

From motives of twisted flag varieties to modular representations of Hecke-type algebras

Kirill Zainoulline (Ottawa)

Let G be a split semisimple linear algebraic group over a field k, let E be a G-torsor over k. Let h be an algebraic oriented cohomology theory in the sense of Levine-Morel (e.g.~Chow ring or an algebraic cobordism). Consider a twisted form E/B of the variety of Borel subgroups G/B. Following Brion's and Kostant-Kumar's results on equivariant cohomology of flag varieties we establish an equivalence between the h-motivic subcategory generated by E/B and the category of projective modules of certain Hecke-type algebra H which depends on the root system of G, its isogeny class, on E, and on the formal group law of the theory h. In particular, taking h to be the Chow groups with finite coefficients F_p and E to be a generic torsor we obtain that all irreducible submodules of the affine nil-Hecke algebra H of G with coefficients in F_p are isomorphic and correspond to the generalized Rost-Voevodsky motive for (G,p).


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