Trace formulae for actions of finite unitary groups on cohomology of Artin–Schreier varieties

Abstract

Associated to a certain additive polynomial, we introduce an Artin–Schreier variety admitting an action of a finite unitary group. We calculate the character of the cohomology as a representation of a finite unitary group. One of our main ingredients is explicit character formulae for Weil representations of unitary groups due to Gérardin. We give another trace formula for a projective hypersurface admitting an action of a finite unitary group.