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On the Mordell-Weil Groups of Jacobians of Hyperelliptic Curves over Certain Elementary Abelian 2-extensions
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  • Journal title : Kyungpook mathematical journal
  • Volume 49, Issue 3,  2009, pp.419-424
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2009.49.3.419
 Title & Authors
On the Mordell-Weil Groups of Jacobians of Hyperelliptic Curves over Certain Elementary Abelian 2-extensions
Moon, Hyun-Suk;
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Let J be the Jacobian variety of a hyperelliptic curve over . 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 -module of infinite rank. In particular, J(M) is not a divisible group. On the other hand, if is an extension of M which contains all the torsion points of J over , then is a divisible group of infinite rank, where is the maximal solvable extension of .
Mordell-Weil groups;hyperelliptic curves;
 Cited by
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