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This article is cited in 4 scientific papers (total in 4 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.
DOI:
https://doi.org/10.4213/sm7790
 Full text:
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English version:
Sbornik: Mathematics, 2012, 203:5, 645–676
Bibliographic databases:
     
UDC:
512.73
MSC: Primary 14F05, 18C15; Secondary 13D09, 18E30
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
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/msb7790https://doi.org/10.4213/sm7790 http://mi.mathnet.ru/eng/msb/v203/i5/p33
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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A. Kuznetsov, A. Perry, “Derived categories of cyclic covers and their branch divisors”, Selecta Math. (N.S.), 23:1 (2017), 389–423
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Tabuada G., “Equivariant Noncommutative Motives”, Ann. K-Theory, 3:1 (2018), 125–156
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Auel A. Bernardara M., “Semiorthogonal Decompositions and Birational Geometry of Del Pezzo Surfaces Over Arbitrary Fields”, Proc. London Math. Soc., 117:1 (2018), 1–64
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Shinder E., “Group Actions on Categories and Elagin'S Theorem Revisited”, Eur. J. Math., 4:1, 1, SI (2018), 413–422
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