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arXiv · 1711.07552

On Jacobians with group action and coverings

Sebastián Reyes-Carocca·Rubí E. Rodríguez
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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 $S_1 \to S_2$ is a regular covering map, then it is also known that the group algebra decomposition of $JS_1$ induces an isogeny decomposition of $JS_2.$ 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.

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Sebastián Reyes-Carocca, Rubí E. Rodríguez. 2017-11-20. On Jacobians with group action and coverings. https://doi.org/10.1007/s00209-019-02263-3

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