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

This article is cited in 4 scientific papers (total in 4 papers)

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
Received in August 2008

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
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\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
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\vol 264
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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. A. Elagin, “Descent theory for semiorthogonal decompositions”, Sb. Math., 203:5 (2012), 645–676  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Lee K.-S., “Exceptional sequences of maximal length on some surfaces isogenous to a higher product”, J. Algebra, 454 (2016), 308–333  crossref  mathscinet  zmath  isi  elib  scopus
    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  crossref  mathscinet  zmath  isi  scopus
    4. Novakovic S., “Tilting Objects on Some Global Quotient Stacks”, J. Commut. Algebr., 10:1 (2018), 107–137  crossref  mathscinet  zmath  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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