LAUSR

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 $$S_1 \rightarrow S_2$$ S 1 → S 2 is a regular covering map, then it is also known that the group algebra decomposition of $$JS_1$$ J S 1 induces an isogeny decomposition of $$JS_2.$$ J S 2 . 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.