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Sbornik: Mathematics, 2012, Volume 203, Issue 5, Pages 645–676
DOI: https://doi.org/10.1070/SM2012v203n05ABEH004238 (Mi sm7790) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Descent theory for semiorthogonal decompositions

A. Elaginab

a A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences
b National Research University "Higher School of Economics"
English version PDF (459 kB) Citations (10)
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DOI: https://doi.org/10.1070/SM2012v203n05ABEH004238
Abstract: We put forward a method for constructing semiorthogonal decompositions of the derived category of $G$-equivariant sheaves on a variety $X$ under the assumption that the derived category of sheaves on $X$ admits a semiorthogonal decomposition with components preserved by the action of the group $G$ on $X$. This method is used to obtain semiorthogonal decompositions of equivariant derived categories for projective bundles and blow-ups with a smooth centre as well as for varieties with a full exceptional collection preserved by the group action. Our main technical tool is descent theory for derived categories.
Bibliography: 12 titles.
Keywords: derived category, semiorthogonal decomposition, descent theory, algebraic variety.
Received: 15.09.2010 and 12.08.2011
Russian version:
Matematicheskii Sbornik, 2012, Volume 203, Number 5, Pages 33–64
DOI: https://doi.org/10.4213/sm7790
Bibliographic databases:
Document Type: Article
UDC: 512.73
MSC: Primary 14F05, 18C15; Secondary 13D09, 18E30
Language: English
Original paper language: Russian
Citation: A. Elagin, “Descent theory for semiorthogonal decompositions”, Mat. Sb., 203:5 (2012), 33–64; Sb. Math., 203:5 (2012), 645–676
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:188
    English version PDF:5
    References:47
    First page:36
     
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