发表机构
Hanoi University of Science and Technology（河内科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文解决了Furio和Lombardo的猜想1.6，从而完成了非CM椭圆曲线在有理数域上的7-adic Galois像的完全分类，证明基于作者2026年6月至9月的AI训练，且为独立完成。
AI 中文摘要
我们解决了Furio和Lombardo的猜想1.6（见[On $7$-adic Galois representations for elliptic curves over $\Q$, Proc.\\ London Math.\\ Soc.\\ (3) \textbf{133} (2026), e70193.]）。作为推论，我们完成了非CM椭圆曲线在$\Q$上的$7$-adic Galois像的分类。证明是作者在2026年6月至2026年9月期间长期AI训练的结果。作者独自完成此项目，未借助任何他人帮助。
英文摘要
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.
Comments30 pages
