Abelian Varieties and Finitely Generated Galois Groups

Bo-Hae Im; Michael Larsen

Abelian Varieties and Finitely Generated Galois Groups

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arxiv 1902.04011 v1 pith:SOZXJE26 submitted 2019-02-11 math.NT

Bo-Hae Im , Michael Larsen This is my paper · ORCID

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keywords abelianfinitelygaloisgeneratedalwaysattackbeencharacteristic

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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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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

On Larsen's conjecture on the ranks of Elliptic Curves
math.NT 2024-11 reject novelty 5.0 of 10

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.

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