Quasi-coherent Hecke category and Demazure descent

Sergey Arkhipov; Tina Kanstrup

Quasi-coherent Hecke category and Demazure descent

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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.

Translated title of the contribution	Quasi-coherent Hecke categori og Demazure descent
Original language	English
Journal	Moscow Mathematical Journal
Volume	15
Issue	2
Pages (from-to)	257-267
Number of pages	11
ISSN	1609-3321
Publication status	Published - 2015

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http://www.mathjournals.org/mmj/2015-015-002/2015-015-002-004.html

Cite this

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title = "Quasi-coherent Hecke category and Demazure descent",

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.",

author = "Sergey Arkhipov and Tina Kanstrup",

year = "2015",

language = "English",

volume = "15",

pages = "257--267",

journal = "Moscow Mathematical Journal",

issn = "1609-3321",

publisher = "Independent University of Moscow",

number = "2",

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TY - JOUR

T1 - Quasi-coherent Hecke category and Demazure descent

AU - Arkhipov, Sergey

AU - Kanstrup, Tina

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

M3 - Journal article

SN - 1609-3321

VL - 15

SP - 257

EP - 267

JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

IS - 2

ER -