Abstract

Given a finite group G and an abelian variety A acted on by G, to any subgroup H of G, we associate an abelian subvariety AH on which the associated Hecke algebra HH for H in G acts. Any irreducible rational representation W˜ of HH induces an abelian subvariety of AH in a natural way. In this paper we give equations for this abelian subvariety. In a special case these equations become much easier. We work out some examples.