This article is cited in 3 papers

Quasi-coherent Hecke category and Demazure Descent

Sergey Arkhipov^a, Tina Kanstrup<sup>b

a</sup> Matematisk Institut, Aarhus Universitet, Ny Munkegade, DK-8000, Århus C, Denmark
^b Centre for Quantum Geometry of Moduli Spaces, Aarhus Universitet, Ny Munkegade, DK-8000, Århus C, Denmark

Abstract: 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 $X$.

Key words and phrases: equivariant coherent sheaves, Demazure functors, Bott–Samelson varieties.

MSC: Primary 14M15; Secondary 20F55, 18E30

Received: May 20, 2014

Language: English

DOI: 10.17323/1609-4514-2015-15-2-257-267

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