Year: 2026
Type: preprint
Abstract: We solve Conjecture 1.6 of Furio and Lombardo [On $7$-adic Galois representations for elliptic curves over $\Q$, Proc.\ London Math.\ Soc.\ (3) \textbf{133} (2026), e70193.]. As a consequence, we complete the classification of $7$-adic Galois images for non-CM elliptic curves over $\Q$. This is the first solved case in Problem 6.2 from Balakrishnan [\emph{Chabauty and beyond: Explicit p-adic methods for rational points}, Proceedings of the International Congress of Mathematicians 2026 - Volume 3: Invited Lectures (Sections 1-4), 321-341, 2026]. The proof is the result of a long AI-training period by the author from June 2026 to September 2026. The author has been working on this project alone without the help of any other.
Source: arXiv (Cornell University)
Author: Xuan, Tho Nguyen
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214766584