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On derived equivalence classes of algebraic varieties

M. Anel·B. Toen
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Abstract

Let $X \to S$ be a miniversal family of smooth and projective varieties and D be a fixed triangulated category. We show that the set of points s in S such that the derived category of the fiber X_s at s is equivalent to D is at most countable. We deduce from this that the derived equivalence classes of smooth and projective complex varieties is at most countable.

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M. Anel, B. Toen. 2007-07-04. On derived equivalence classes of algebraic varieties. https://arxiv.org/abs/math/0611545

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