  We consider derived invariants of varieties in positive characteristic
arising from topological Hochschild homology. Using theory developed by Ekedahl
and Illusie-Raynaud in their study of the slope spectral sequence, we examine
the behavior under derived equivalences of various $p$-adic quantities related
to Hodge-Witt and crystalline cohomology groups, including slope numbers,
domino numbers, and Hodge-Witt numbers. As a consequence, we obtain
restrictions on the Hodge numbers of derived equivalent varieties, partially
extending results of Popa-Schell to positive characteristic.
