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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"
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
Citation:
A. Elagin, “Descent theory for semiorthogonal decompositions”, Mat. Sb., 203:5 (2012), 33–64; Sb. Math., 203:5 (2012), 645–676
Linking options:
https://www.mathnet.ru/eng/sm7790https://doi.org/10.1070/SM2012v203n05ABEH004238 https://www.mathnet.ru/eng/sm/v203/i5/p33
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Abstract page: | 519 | Russian version PDF: | 188 | English version PDF: | 5 | References: | 47 | First page: | 36 |
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