Periodic subvarieties of semiabelian varieties and annihilators of irreducible representations

Abstract

Let G be a semiabelian variety defined over a field of characteristic 0, endowed with an endomorphism Φ. We prove there is no proper subvariety Y⊂G which intersects the orbit of each periodic point of G under the action of Φ. As an application, we are able to give a topological characterization of the annihilator ideals of irreducible representations in certain skew polynomial algebras.