Larsen's conjecture for elliptic curves over ℚ with analytic rank at most 1

2025/02/26 by Choi, Seokhyun, Bo‐Hae Im, Im, Bo-Hae
Mathematics · #11G05 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2502.18761

openalex publication_date 2025/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove Larsen's conjecture for elliptic curves over ℚ with analytic rank at most 1. Specifically, let E/ℚ be an elliptic curve over ℚ. If E/ℚ has analytic rank at most 1, then we prove that for any topologically finitely generated subgroup G of Gal(ℚ/ℚ), the rank of E over the fixed subfield ℚ^G of ℚ under G is infinite.

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