Actions of finite groups on algebraic curves have been extensively investigated. In particular, a formulaof Chevalley and Weil determines the representation of the automorphism group of a complex smoothprojective curve on the space of holomorphic differential forms. By contrast, little seems to be known about actions of finite group schemes in positive characteristics.
The talk will discuss some basic results in this setting, and then present a version of the Chevalley-Weil formula with applications to algebraic surfaces.
