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Izv. RAN. Ser. Mat., 2009, Volume 73, Issue 5, Pages 37–66 (Mi izv2772)  

This article is cited in 8 scientific papers (total in 8 papers)

Semiorthogonal decompositions of derived categories of equivariant coherent sheaves

A. Elagin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Let $X$ be an algebraic variety with an action of an algebraic group $G$. Suppose that $X$ has a full exceptional collection of sheaves and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of the bounded derived category of $G$-equivariant coherent sheaves on $X$ into components that are equivalent to the derived categories of twisted representations of $G$. If the group is finite or reductive over an algebraically closed field of characteristic 0, this gives a full exceptional collection in the derived equivariant category. We apply our results to particular varieties such as projective spaces, quadrics, Grassmannians and del Pezzo surfaces.

Keywords: semiorthogonal decomposition, exceptional collection, twisted sheaf.

DOI: https://doi.org/10.4213/im2772

Full text: PDF file (704 kB)
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English version:
Izvestiya: Mathematics, 2009, 73:5, 893–920

Bibliographic databases:

UDC: 512.732
MSC: 14F08, 14M15, 18E30
Received: 21.02.2008

Citation: A. Elagin, “Semiorthogonal decompositions of derived categories of equivariant coherent sheaves”, Izv. RAN. Ser. Mat., 73:5 (2009), 37–66; Izv. Math., 73:5 (2009), 893–920

Citation in format AMSBIB
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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. Krug A., Sosna P., “on the Derived Category of the Hilbert Scheme of Points on An Enriques Surface”, Sel. Math.-New Ser., 21:4 (2015), 1339–1360  crossref  mathscinet  zmath  isi  elib
    3. Galkin S. Katzarkov L. Mellit A. Shinder E., “Derived Categories of Keum'S Fake Projective Planes”, Adv. Math., 278 (2015), 238–253  crossref  mathscinet  zmath  isi  elib
    4. 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
    5. 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
    6. Cho Ch.-H., Hong H., “Finite Group Actions on Lagrangian Floer Theory”, J. Symplectic Geom., 15:2 (2017), 307–420  crossref  mathscinet  zmath  isi
    7. Novakovic S., “Tilting Objects on Some Global Quotient Stacks”, J. Commut. Algebr., 10:1 (2018), 107–137  crossref  mathscinet  zmath  isi
    8. 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  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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