English

The modular approach to Diophantine equations over totally real fields

Number Theory 2024-01-09 v1

Abstract

Wiles' proof of Fermat's last theorem initiated a powerful new approach towards the resolution of certain Diophantine equations over Q\mathbb{Q}. Numerous novel obstacles arise when extending this approach to the resolution of Diophantine equations over totally real number fields. We give an extensive overview of these obstacles as well as providing a survey of existing methods and results in this area.

Keywords

Cite

@article{arxiv.2401.03099,
  title  = {The modular approach to Diophantine equations over totally real fields},
  author = {Maleeha Khawaja and Samir Siksek},
  journal= {arXiv preprint arXiv:2401.03099},
  year   = {2024}
}
R2 v1 2026-06-28T14:09:57.933Z