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 Tr. Mat. Inst. Steklova, 2009, Volume 264, Pages 63–68 (Mi tm802)

Equivariant Derived Category of Bundles of Projective Spaces

A. Elagin

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

Abstract: We give an analog of D. O. Orlov's theorem on semiorthogonal decompositions of the derived category of projective bundles for the case of equivariant derived categories. Under the condition that the action of a finite group on the projectivization $X$ of a vector bundle $E$ is compatible with the twisted action of the group on the bundle $E$, we construct a semiorthogonal decomposition of the derived category of equivariant coherent sheaves on $X$ into subcategories equivalent to the derived categories of twisted sheaves on the base scheme.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 264, 56–61

Bibliographic databases:

UDC: 512.7

Citation: A. Elagin, “Equivariant Derived Category of Bundles of Projective Spaces”, Multidimensional algebraic geometry, Collected papers. Dedicated to the Memory of Vasilii Alekseevich Iskovskikh, Corresponding Member of the Russian Academy of Sciences, Tr. Mat. Inst. Steklova, 264, MAIK Nauka/Interperiodica, Moscow, 2009, 63–68; Proc. Steklov Inst. Math., 264 (2009), 56–61

Citation in format AMSBIB
\Bibitem{Ela09} \by A.~Elagin \paper Equivariant Derived Category of Bundles of Projective Spaces \inbook Multidimensional algebraic geometry \bookinfo Collected papers. Dedicated to the Memory of Vasilii Alekseevich Iskovskikh, Corresponding Member of the Russian Academy of Sciences \serial Tr. Mat. Inst. Steklova \yr 2009 \vol 264 \pages 63--68 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm802} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2590835} \elib{http://elibrary.ru/item.asp?id=11807017} \transl \jour Proc. Steklov Inst. Math. \yr 2009 \vol 264 \pages 56--61 \crossref{https://doi.org/10.1134/S0081543809010076} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000265834800006} \elib{http://elibrary.ru/item.asp?id=13615423} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-65749115027} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. Elagin, “Descent theory for semiorthogonal decompositions”, Sb. Math., 203:5 (2012), 645–676
2. Lee K.-S., “Exceptional sequences of maximal length on some surfaces isogenous to a higher product”, J. Algebra, 454 (2016), 308–333
3. Kim H.K., Kim Yu.-H., Lee K.-S., “Quasiphantom categories on a family of surfaces isogenous to a higher product”, J. Algebra, 473 (2017), 591–606
4. Novakovic S., “Tilting Objects on Some Global Quotient Stacks”, J. Commut. Algebr., 10:1 (2018), 107–137
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