Hodge numbers are not derived invariants in positive characteristic

Over the complex numbers, the Hodge numbers of a 3-fold are invariants of the derived category, but I will show that this fails over \overline{F_3}. The counterexample is a pair of 3-folds fibered over P^1 in Abelian surfaces, similar to the example of Gross, Popescu, Bak, and Schnell which shows that the fundamental group and Brauer group are not derived invariants. There are also connections with special cubic fourfolds of discriminant 18. This is joint work with Dan Bragg.