Darmon's Program: A survey
Number Theory
2025-07-22 v1
Abstract
We give an overview of Darmon's program for resolving families of generalized Fermat equations with one varying exponent and survey what is currently known about this approach based on recent work of Billerey-Chen-Dieulefait-Freitas and Chen-Koutsianas. Additionally, we provide background material which is helpful to understand and apply the methods developed in these recent works. In particular, we explain the basic strategy for and simplified examples of each of the steps that is required in order to resolve a family of generalized Fermat equations.
Cite
@article{arxiv.2507.15149,
title = {Darmon's Program: A survey},
author = {Imin Chen and Angelos Koutsianas},
journal= {arXiv preprint arXiv:2507.15149},
year = {2025}
}
Comments
38 pages; publication of the proceedings in which this article been accepted has been delayed so we have made this version available in the meantime