We prove that if two abelian varieties have equivalent derived categories then the derived categories of the smooth stacks associated to the corresponding Kummer varieties are equivalent as well. The second main result establishes necessary and sufficient conditions for the existence of equivalences between the twisted derived categories of two Kummer surfaces in terms of Hodge isometries between the generalized transcendental lattices of the corresponding abelian surfaces.
Derived categories and Kummer varieties / P. Stellari. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 256:2(2007 Jun), pp. 425-441.
Derived categories and Kummer varieties
P. StellariPrimo
2007
Abstract
We prove that if two abelian varieties have equivalent derived categories then the derived categories of the smooth stacks associated to the corresponding Kummer varieties are equivalent as well. The second main result establishes necessary and sufficient conditions for the existence of equivalences between the twisted derived categories of two Kummer surfaces in terms of Hodge isometries between the generalized transcendental lattices of the corresponding abelian surfaces.
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