Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derived categories and Kummer varieties   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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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio