LAUSR

Abstract Let V be a quasiprojective variety defined over F q , and let ϕ : V → V be an endomorphism of V that is also defined over F q . Let G be a finite subgroup of Aut F q ( V ) with the property that ϕ commutes with every element of G. We show that idempotent relations in the group ring Q [ G ] give relations between the periodic point counts for the maps induced by ϕ on quotients of V by various subgroups of G. We also show that periodic point counts for the endomorphism on V / G induced by ϕ are related to periodic point counts on V and all of its twists by G.