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Mosc. Math. J., 2015, Volume 15, Number 2, Pages 257–267 (Mi mmj557)  

This article is cited in 1 scientific paper (total in 1 paper)

Quasi-coherent Hecke category and Demazure Descent

Sergey Arkhipova, Tina Kanstrupb

a 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.

DOI: https://doi.org/10.17323/1609-4514-2015-15-2-257-267

Full text: http://www.mathjournals.org/.../2015-015-002-004.html
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Bibliographic databases:

MSC: Primary 14M15; Secondary 20F55, 18E30
Received: May 20, 2014
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Citation: Sergey Arkhipov, Tina Kanstrup, “Quasi-coherent Hecke category and Demazure Descent”, Mosc. Math. J., 15:2 (2015), 257–267

Citation in format AMSBIB
\Bibitem{ArkKan15}
\by Sergey~Arkhipov, Tina~Kanstrup
\paper Quasi-coherent Hecke category and Demazure Descent
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 2
\pages 257--267
\mathnet{http://mi.mathnet.ru/mmj557}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-2-257-267}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3427422}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000361607300004}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. Arkhipov, T. Kanstrup, “Equivariant matrix factorizations and Hamiltonian reduction”, Bull. Korean. Math. Soc., 54:5 (2017), 1803–1825  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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