On the canonical representation of curves in positive characteristic

摘要

Given a smooth curve, the canonical representation of its automorphism group is given by the natural action of the automorphisms on the space of global regular 1-forms. In this paper, we study an explicit set of curves in positive characteristic with irreducible canonical representation whose genus is unbounded. Additionally, we study the implications this has for the de Rham hypercohomology as a representation of the automorphism group.