Periodic subvarieties of semiabelian varieties and annihilators of irreducible representations

Let G be a semiabelian variety defined over a field of characteristic 0, endowed with an endornorphisrn Phi. We prove there is no proper subvariety Y subset of G which intersects the orbit of each periodic point of G under the action of Phi. As an application, we are able to give a topological characterization of the annihilator ideals of irreducible representations in certain skew polynomial algebras. Crown Copyright (C) 2019 Published by Elsevier Inc. All rights reserved.