%0 Journal Article %T Derived categories of Fano threefolds %A Alexander Kuznetsov %J Mathematics %D 2008 %I arXiv %X We consider the structure of the derived categories of coherent sheaves on Fano threefolds with Picard number 1 and describe a strange relation between derived categories of different threefolds. In the Appendix we discuss how the ring of algebraic cycles of a smooth projective variety is related to the Grothendieck group of its derived category. %U http://arxiv.org/abs/0809.0225v1