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arXiv · 2012.12666

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

Nuno Freitas·Alain Kraus·Samir Siksek
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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.

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Nuno Freitas, Alain Kraus, Samir Siksek. 2021-02-17. Local criteria for the unit equation and the asymptotic Fermat's Last Theorem. https://doi.org/10.1073/pnas.2026449118

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