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

This article is cited in 54 scientific papers (total in 54 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.


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English version:
Russian Mathematical Surveys, 2003, 58:3, 511–591

Bibliographic databases:

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
\by D.~O.~Orlov
\paper Derived categories of coherent sheaves and equivalences between them
\jour Uspekhi Mat. Nauk
\yr 2003
\vol 58
\issue 3(351)
\pages 89--172
\jour Russian Math. Surveys
\yr 2003
\vol 58
\issue 3
\pages 511--591

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