Cycle classes on the moduli of K3 surfaces in positive characteristic

This paper provides explicit closed formulas in terms of tautological classes for the cycle classes of the height and Artin invariant strata in families of K3 surfaces. The proof is uniform for all strata and uses a flag space as the computations in Ekedahl and van der Geer (Algebra, arithmetic and geometry, progress in mathematics, vol. 269-270, Birkhauser, Basel, 2010) for the Ekedahl-Oort strata for families of abelian varieties, but employs a Pieri formula to determine the push down to the base space.