Derived categories of coherent sheaves and equivalences between them

D O Orlov
2003 Russian Mathematical Surveys  
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:10.1070/rm2003v058n03abeh000629 fatcat:ldshr5qesjctlpjotrpe23dr3q