Journal of Mathematical Sciences

, Volume 84, Issue 5, pp 1361–1381 | Cite as

Equivalences of derived categories and K3 surfaces

  • D. O. Orlov


We consider derived categories of coherent sheaves on smooth projective variaties. We prove that any equivalence between them can be represented by an object on the product. Using this, we give a necessary and sufficient condition for equivalence of derived categories of two K3 surfaces.


Abelian Category Coherent Sheave Triangulate Category Smooth Projective Variety Canonical Morphism 
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© Plenum Publishing Corporation 1997

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  • D. O. Orlov

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