On the twist of abelian varieties defined by the Galois extension of prime degree (Q1320158)

Let \(A\) be an abelian variety over a field \(k\). Furthermore let \(k(t)\) be the rational function field over \(k\) and \(k(C)/ k(t)\) be a Kummer extension of prime degree corresponding to a curve \(C\) with Jacobian variety \(J(C)\). Consider the abelian variety \(\widetilde {A}\) over \(k(t)\) which is the twist of \(A\) by the extension \(k(C)/ k(t)\). The author shows that the Mordell-Weil group \(\widetilde {A} (k(t))\) is the direct sum of a subgroup of \(\Hom (J(C), A)\) and certain \(k\)-rational division points of \(A\).