Geodesic
Derived categories of coherent sheaves and equivalences between them
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 58 (2003) no. 3, pp. 511-591

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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. 
@article{RM_2003_58_3_a2,
     author = {D. O. Orlov},
     title = {Derived categories of coherent sheaves and equivalences between them},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {511--591},
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     volume = {58},
     number = {3},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2003_58_3_a2/}
}
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D. O. Orlov. Derived categories of coherent sheaves and equivalences between them. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 58 (2003) no. 3, pp. 511-591. http://geodesic.mathdoc.fr/item/RM_2003_58_3_a2/