On the Mordell-Weil Groups of Jacobians of Hyperelliptic Curves over Certain Elementary Abelian 2-extensions

Hyun-Suk Moon
2009 Kyungpook Mathematical Journal  
Let J be the Jacobian variety of a hyperelliptic curve over Q. Let M be the field generated by all square roots of rational integers over a finite number field K. Then we prove that the Mordell-Weil group J(M ) is the direct sum of a finite torsion group and a free Z-module of infinite rank. In particular, J(M ) is not a divisible group. On the other hand, if M is an extension of M which contains all the torsion points of J over Q, then J( M sol )/J( M sol )tors is a divisible group of infinite
more » ... rank, where M sol is the maximal solvable extension of M .
doi:10.5666/kmj.2009.49.3.419 fatcat:mckvksx53vd5bowkwvgrfhf3rm