Derived categories of coherent sheaves on abelian varieties and equivalences between them

Abstract

We study derived categories of coherent sheaves on abelian varieties. We give a criterion for the equivalence of the derived categories on two abelian varieties. We describe the autoequivalence group for the derived category of coherent sheaves of an abelian variety.

26 pages, TeX file, published in Izvestiya: Mathematics, 66 (2002), 3, 569-594, translated by journal. The last version differs from the previous one, which is completely identical to the journal version, only by the addition of an Appendix with a proof of the statement formulated in the article as an easily provable property

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