2015/05/26 by Alexander Neshitov, Victor Petrov, Neshitov, Alexander +5
Mathematics · #14C15 #14F43 #14M15 #20C08 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1505.07083
openalex publication_date 2015/05/26 · openalex created_date 2022/08/22 · openalex updated_date 2026/07/28
Let G be a split semisimple linear algebraic group over a field k0. Let E be\na G-torsor over a field extension k of k0. Let h be an algebraic oriented\ncohomology theory in the sense of Levine-Morel. Consider a twisted form E/B of\nthe variety of Borel subgroups G/B over k.\n Following the Kostant-Kumar results on equivariant cohomology of flag\nvarieties we establish an isomorphism between the Grothendieck groups of the\nh-motivic subcategory generated by E/B and the category of finitely generated\nprojective modules of certain Hecke-type algebra H which depends on the root\ndatum of G, on the torsor E and on the formal group law of the theory h.\n In particular, taking h to be the Chow groups with finite coefficients Fp and\nE to be a generic G-torsor we prove that all indecomposable submodules of an\naffine nil-Hecke algebra H of G with coefficients in Fp are isomorphic to each\nother and correspond to the (non-graded) generalized Rost-Voevodsky motive for\n(G,p).\n