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Uspekhi Mat. Nauk, 2003, Volume 58, Issue 3(351), Pages 89–172 (Mi umn629)  

This article is cited in 45 scientific papers (total in 45 papers)

Derived categories of coherent sheaves and equivalences between them

D. O. Orlov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: This paper studies the derived categories of coherent sheaves on smooth complete algebraic varieties and equivalences between them. We prove that every equivalence of categories is represented by an object on the product of the varieties. This result is applied to describe the Abelian varieties and K3 surfaces that have equivalent derived categories of coherent sheaves.

DOI: https://doi.org/10.4213/rm629

Full text: PDF file (838 kB)
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English version:
Russian Mathematical Surveys, 2003, 58:3, 511–591

Bibliographic databases:

Document Type: Article
UDC: 512.73+512.664
MSC: Primary 14F05, 18E30; Secondary 14J28, 14K05
Received: 05.02.2003

Citation: D. O. Orlov, “Derived categories of coherent sheaves and equivalences between them”, Uspekhi Mat. Nauk, 58:3(351) (2003), 89–172; Russian Math. Surveys, 58:3 (2003), 511–591

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:
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    3. D. O. Orlov, “Derived categories of coherent sheaves and motives”, Russian Math. Surveys, 60:6 (2005), 1242–1244  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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    24. S. Gorchinskiy, D. Orlov, “GGeometric phantom categories”, Publ. Math. Inst. Hautes Études Sci., 117:1 (2013), 329–349  crossref  mathscinet  zmath  isi  scopus
    25. U. V. Dubey, V. M. Mallick, “Reconstruction of a Superscheme From its Derived Category”, J. Ramanujan Math. Soc., 28:2 (2013), 179–193  mathscinet  zmath  isi  elib
    26. V. Brînzănescu, A. D. Halanay, G. Trautmann, “Vector bundles on non-Kaehler elliptic principal bundles”, Ann. Inst. Fourier (Grenoble), 63:3 (2013), 1033–1054  crossref  mathscinet  zmath  isi  scopus  scopus
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    34. Marcello Bernardara, Gonçalo Tabuada, “From semi-orthogonal decompositions to polarized intermediate Jacobians via Jacobians of noncommutative motives”, Mosc. Math. J., 16:2 (2016), 205–235  mathnet  mathscinet
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    40. Honigs K., “Derived Equivalence, Albanese Varieties, and the Zeta Functions of 3-Dimensional Varieties”, Proc. Amer. Math. Soc., 146:3 (2018), 1005–1013  crossref  mathscinet  zmath  isi  scopus  scopus
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    44. D. O. Orlov, “Derived noncommutative schemes, geometric realizations, and finite dimensional algebras”, Russian Math. Surveys, 73:5 (2018), 865–918  mathnet  crossref  crossref  isi  elib
    45. Masaharu K., “On the Frobenius Direct Image of the Structure Sheaf of a Homogeneous Projective Variety”, J. Algebra, 512 (2018), 160–188  crossref  mathscinet  zmath  isi  scopus
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