On the supersingular divisors of nilpotent admissible indigenous bundles

Abstract

In the present paper, we give a characterization of the supersingular divisors [i.e., the zero loci of the Hasse invariants] of nilpotent admissible/ordinary indigenous bundles on hyperbolic curves. By applying the characterization, we also obtain lists of the nilpotent indigenous bundles on certain hyperbolic curves. Moreover, we prove the hyperbolic ordinariness of certain hyperbolic curves.