On the Mordell-Weil group of certain abelian varieties defined over the rational function field
The aim of this paper is to prove the following theorem, which generalizes a recent result of \textit{C. Wajngurt} [J. Number Theory 23, 80-85 (1986; Zbl 0584.14019)]: Let C be a hyperelliptic curve over a field k, and let A be an abelian variety over k. Denote by \(A_ b\) the twist of A defined by the quadratic extension \(k(C)/k({\mathbb{P}}^ 1)\). Then we have an isomorphism of abelian groups \(A_ b(k(t))\cong Hom_ K(J(C),A)\oplus A_ 2(k),\) where \(A_ 2(k)\) denotes the group of k- rational 2-division points of A.
scientific article; zbMATH DE number 4204539