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- W151775571 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." @default.
- W151775571 created "2016-06-24" @default.
- W151775571 creator A5073182985 @default.
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- W151775571 date "1982-01-01" @default.
- W151775571 modified "2023-10-16" @default.
- W151775571 title "Mordell-Weil Groups of Elliptic Curves Over Cyclotomic Fields" @default.
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- W151775571 doi "https://doi.org/10.1007/978-1-4899-6699-5_15" @default.
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