Hodge numbers are not derived invariants in positive characteristic

We study a pair of Calabi–Yau threefolds X and M , fibered in non-principally polarized Abelian surfaces and their duals, and an equivalence D b ( X ) ≅ D b ( M ) , building on work of Gross, Popescu, Bak, and Schnell. Over the complex numbers, X is simply connected while π 1 ( M ) = ( Z / 3 ) 2 . In characteristic 3, we find that X and M have different Hodge numbers, which would be impossible in characteristic 0. In an appendix, we give a streamlined proof of Abuaf’s result that the ring H ∗ ( O ) is a derived invariant of complex threefolds and fourfolds. A second appendix by Alexander Petrov gives a family of higher-dimensional examples to show that h 0 , 3 is not a derived invariant in any positive characteristic.