On the asymptotic Fermat's Last Theorem over number fields
Number Theory
2016-11-01 v3
Abstract
Assuming two deep but standard conjectures from the Langlands Programme, we prove that the asymptotic Fermat's Last Theorem holds for imaginary quadratic fields Q(\sqrt{-d}) with -d=2, 3 mod 4. For a general number field K, again assuming standard conjectures, we give a criterion based on the solutions to a certain S-unit equation, which if satisfied implies the asymptotic Fermat's Last Theorem.
Cite
@article{arxiv.1609.04458,
title = {On the asymptotic Fermat's Last Theorem over number fields},
author = {Mehmet Haluk Sengun and Samir Siksek},
journal= {arXiv preprint arXiv:1609.04458},
year = {2016}
}