Abstract

Let S be a compact Riemann surface and let H be a finite group. It is known that if H acts on S, then there is a H-equivariant isogeny decomposition of the Jacobian variety JS of S, called the group algebra decomposition of JS with respect to H. If S1→ S2 is a regular covering map, then it is also known that the group algebra decomposition of JS1 induces an isogeny decomposition of JS2. In this article we deal with the converse situation. More precisely, we prove that the group algebra decomposition can be lifted under regular covering maps, under appropriate conditions.