The paper proves, for a restricted family of automorphisms, that the Mordell-Weil group of an elliptic curve over the fixed field has infinite rank.
Abelian Varieties and Finitely Generated Galois Groups
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abstract
This paper surveys the methods that have been used to attack the conjecture, still open, that an abelian variety over a characteristic $0$ field with finitely generated Galois group is always of infinite rank.
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2024 1verdicts
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On Larsen's conjecture on the ranks of Elliptic Curves
The paper proves, for a restricted family of automorphisms, that the Mordell-Weil group of an elliptic curve over the fixed field has infinite rank.