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arXiv · 1609.04458

On the asymptotic Fermat's Last Theorem over number fields

Mehmet Haluk Sengun·Samir Siksek
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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.

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Mehmet Haluk Sengun, Samir Siksek. 2016-09-14. On the asymptotic Fermat's Last Theorem over number fields. https://arxiv.org/abs/1609.04458

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