Supersingular curves on Picard modular surfaces modulo an inert prime
  We study the supersingular curves on Picard modular surfaces modulo a prime $p$ which is inert in the underlying quadratic imaginary field. We analyze the automorphic vector bundles in characteristic $p$, and as an application derive a formula relating the number of irreducible components in the supersingular locus to the second Chern class of the surface. 
Ehud de Shalit and Eyal Goren
math.NT