Algebra/Topology Seminar

Speaker: Tina Kanstrup (Aarhus).

Title: Demazure descent theory.

Abstract: We recall the classical notion of Demazure operators acting on the equivariant K-theory of a smooth manifold with an action of a reductive Lie group. Then we propose a categorification of the algebra generated by Demazure operators and introduce the notion of Demazure Descent Data (DDD) on a category. Let G be a reductive algebraic group with a Borel subgroup B. We explain how DDD arises naturally from a monoidal action of the tensor category of B \times B-equivariant quasi-coherent sheaves on G on a category. A natural example of such an action is provided by the derived category of B-equivariant quasi-coherent sheaves on a scheme X with a G-action. It turns out that the subcategory of G-equivariant quasi-coherent sheaves on X can be described in terms of the DDD. Time permitting we will discuss some further directions. This is joint work with Sergey Arkhipov."