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 their duals, an equivalence $$D^b(X) \cong D^b(M)$$ , building on work Gross, Popescu, Bak, Schnell. Over the complex numbers, is simply connected while $$\pi _1(M) = (\mathbf {Z}/3)^2$$ . In characteristic 3, we find that M have different Hodge which would be impossible 0. appendix, give streamlined proof Abuaf’s result ring $$\mathrm{H}^{*}({\mathscr {O}})$$ derived invariant fourfolds. A second appendix by Alexander Petrov gives family higher-dimensional examples to show $$h^{0,3}$$ not any positive characteristic.