A Mordell-Weil theorem for abelian varieties over fields generated by torsion points

Michael Larsen

A Mordell-Weil theorem for abelian varieties over fields generated by torsion points

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arxiv math/0503378 v1 pith:IGN6TSR5 submitted 2005-03-18 math.NT

Michael Larsen This is my paper · ORCID

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keywords abeliantorsiongeneratedpointsextensionfieldfieldsfree

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If A is an abelian variety over a number field K, and L is a (possibly infinite) extension of K generated by torsion points of A, then the quotient of A(L) by its torsion subgroup is a free abelian group.

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Elliptic curves and finitely generated Galois groups
math.NT 2025-10 conditional novelty 7.0 of 10

If the Galois group of a field is finitely generated, every elliptic curve over it has infinite Mordell–Weil rank.

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