  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 pi_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.
