arXiv Analytics

Sign in

arXiv:2012.12666 [math.NT]AbstractReferencesReviewsResources

On local criteria for the unit equation and the asymptotic Fermat's Last Theorem

Nuno Freitas, Alain Kraus, Samir Siksek

Published 2020-12-23Version 1

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.

Categories: math.NT
Subjects: 11D41
Related articles: Most relevant | Search more
arXiv:1609.04458 [math.NT] (Published 2016-09-14)
On the asymptotic Fermat's Last Theorem over number fields
arXiv:1307.3162 [math.NT] (Published 2013-07-11, updated 2014-07-16)
The Asymptotic Fermat's Last Theorem for Five-Sixths of Real Quadratic Fields
arXiv:2404.09171 [math.NT] (Published 2024-04-14)
On the solutions of the generalized Fermat equation over totally real number fields

Links

Toolbox