Work

Analytic rank-one elliptic curves over function fields and their rank over certain ring class fields

Year: 2026

Type: preprint

Abstract: Let $E/k$ be a non-isotrivial elliptic curve over a global function field $k$ of characteristic $p>3$, and $G\subset \mathrm{Gal}(k^{\mathrm{sep}}/k)$ be a topologically finitely generated subgroup. We prove that if $E/k$ has analytic rank $1$, then its rank over the fixed subfield $L^G$ is infinite, where $L$ is the infinite ring class extension of some finite separable extension $K/k$. If $E/k$ has analytic rank $0$, then we prove that the same holds provided there exists an imaginary quadratic extension $K/k$ such that $E/K$ has analytic rank $1$ and satisfies the Heegner hypothesis.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2603.29686

Authors: Choi, Seokhyun, Im, Bo-Hae, Kim, Beomho

Institution: Korea Advanced Institute of Science and Technology

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Research Foundation, National Research Foundation of Korea, Ministry of Science and ICT, South Korea

Award: G295362363

OpenAlex ID: W7147717866

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