Asymptotic Fermat's Last Theorem over Number Fields

Haluk Sengun (Sheffield)

Frank Adams 1,

Assuming two deep but standard reciprocity conjectures from the Langlands Programme, we prove that the asymptotic Fermat's Last Theorem holds over (most) imaginary quadratic fields. For a general number field K, we give a criterion based on the solutions to a certain S-unit equation, which if satisfied implies, again assuming the same standard conjectures, the asymptotic Fermat's Last Theorem. This is joint work with Samir Siksek.
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