The cycle class of the supersingular locus

Deuring gave a classical formula for the number of supersingular elliptic curves
in characteristic p. We generalize this to a formula for the cycle class of the
supersingular locus in the moduli space of principally polarized abelian varieties
of given dimension g. The formula determines the class up to a multiple and shows
that it lies in the tautological ring. We also give the multiple for g up to 4.
This is joint work with S. Harashita.