Local criteria for the unit equation and the asymptotic Fermat's Last Theorem
Number Theory
2022-05-11 v2
Abstract
Let F be a totally real number field of odd degree. We prove several purely local criteria for the asymptotic Fermat's Last Theorem to hold over F, and also for the non-existence of solutions to the unit equation over F. For example, if 2 totally ramifies and 3 splits completely in F, then the asymptotic Fermat's Last Theorem holds over F.
Keywords
Cite
@article{arxiv.2012.12666,
title = {Local criteria for the unit equation and the asymptotic Fermat's Last Theorem},
author = {Nuno Freitas and Alain Kraus and Samir Siksek},
journal= {arXiv preprint arXiv:2012.12666},
year = {2022}
}