Abstract
Let E be an elliptic curve defined over Q. For any field F containing Q let E(F) denote the group of points of E rational over F. The Mordel1-Weil theorem asserts that if F is a finite extension of Q then E(F) is finitely generated. Our main result shows that for a large class of elliptic curves over Q, and for certain infinite abelian extensions F of Q, the group E(F) remains finitely generated. it should be noted that the torsion subgroup of E(F) over such fields has been studied by Ribet. As a special case of a much more general theorem [16] he has proved that, for any elliptic curve E over Q and any abelian extension F of Q, the group E(F)tors is finite.
Supported by an N.S.F. postdoctoral fellowship.
Supported by N.S.F. Grant MCS77-I8723 A04.
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Rubin, K., Wiles, A. (1982). Mordell-Weil Groups of Elliptic Curves Over Cyclotomic Fields. In: Koblitz, N. (eds) Number Theory Related to Fermat’s Last Theorem. Progress in Mathematics, vol 26. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-6699-5_15
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DOI: https://doi.org/10.1007/978-1-4899-6699-5_15
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