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Quasi-coherent Hecke category and Demazure descent

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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.
Translated title of the contributionQuasi-coherent Hecke categori og Demazure descent
Original languageEnglish
JournalMoscow Mathematical Journal
Pages (from-to)257-267
Number of pages11
Publication statusPublished - 2015

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