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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.

Original language | English |
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Journal | Moscow Mathematical Journal |
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Volume | 15 |
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Issue number | 2 |
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Pages (from-to) | 257-267 |
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Number of pages | 11 |
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ISSN | 1609-3321 |
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State | Published - 2015 |
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ID: 84174166