In this paper, using a generalization of the notion of Prym variety for covers of quasi-projective varieties, we prove a structure theorem for the Mordell-Weil group of the abelian varieties over function fields that are twists of Abelian varieties by Galois covers of irreducible quasi-projective varieties. In particular, the resutls we obtain contribute in the construction of Jacobians (of covers of the projective line) of high rank.

中文翻译：

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函数域上的阿贝尔簇和 Prym 簇的有理点

在本文中，我们利用对拟射影簇的覆盖的 Prym 簇概念的推广，证明了阿贝尔簇在函数域上的 Mordell-Weil 群的结构定理，该函数域是由不可约的伽罗瓦覆盖的阿贝尔簇的扭曲。准射影变种。特别是，我们获得的结果有助于构建高阶雅可比行列式（投影线的覆盖）。