On the supersingular loci of quaternionic Siegel space
  The paper studies the supersingular locus of the characteristic p moduli space of principally polarized abelian 8-folds that are equipped with an action of a maximal order in a quaternion algebra, that is non-split at the infinite place, but split at p. The main result is that its irreducible components are Fermat surfaces of degree p+1. 
Oliver Bueltel
math.AG