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Moscow Mathematical Journal

Volume 15, Issue 2, April–June 2015  pp. 257–267.

Quasi-Coherent Hecke Category and Demazure Descent

Authors:  Sergey Arkhipov (1) and Tina Kanstrup
Author institution:(1) Matematisk Institut, Aarhus Universitet, Ny Munkegade, DK-8000, Århus C, Denmark
(2) Centre for Quantum Geometry of Moduli Spaces, Aarhus Universitet, Ny Munke gade, DK-8000, Århus C, Denmark


Let G be a reductive algebraic group with a Borel subgroup B. We define the quasi-coherent Hecke category for the pair (G, B). For any regular Noetherian G-scheme X we construct a monoidal action of the Hecke category on the derived category of B-equivariant quasi-coherent sheaves on X. Using the action we define the Demazure Descent Data on the latter category and prove that the Descent category is equivalent to the derived category of G-equivariant sheaves on X.

2010 Math. Subj. Class. Primary: 14M15; Secondary: 20F55, 18E30.

Keywords: Equivariant coherent sheaves, Demazure functors, Bott–Samelson varieties

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