English

Integral Points on Elliptic Curves and Modularity

Number Theory 2020-06-09 v1

Abstract

In this paper we prove the finiteness of the set of S-integral points of a punctured rational elliptic curve without complex multiplication using the Chabauty-Kim method. This extends previous results of Kim in the complex multiplication case. The key input of our approach is the use of modularity techniques to prove the vanishing of certain Selmer groups involved in the Chabauty-Kim method.

Keywords

Cite

@article{arxiv.2006.04758,
  title  = {Integral Points on Elliptic Curves and Modularity},
  author = {Federico Amadio Guidi},
  journal= {arXiv preprint arXiv:2006.04758},
  year   = {2020}
}

Comments

11 pages. Comments are welcome!

R2 v1 2026-06-23T16:09:15.711Z