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arXiv · 2208.14378

Derived equivalences over base schemes and support of complexes

Max Lieblich·Martin Olsson
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Abstract

Let $X$ and $Y$ be smooth projective varieties over a field $k$ admitting morphisms $f:X \to T$ and $g:Y \to T$ to a third variety $T$. We formulate conditions on a derived equivalence $\Phi:D(X) \to D(Y)$ ensuring that $\Phi$ is induced by a complex $P \in D(X \times_T Y )$, defining derived equivalences between the fibers of $f$ and $g$. We apply our results to the canonical fibration and albanese fibration.

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Max Lieblich, Martin Olsson. 2022-08-30. Derived equivalences over base schemes and support of complexes. https://arxiv.org/abs/2208.14378

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