STNB2017, (31st edition)
Asymptotic Fermat's Last Theorem over Number Fields
Presenters
Haluk Sengun
Abstract
Assuming two deep but standard reciprocity conjectures from the Langlands Programme, we prove that the asymptotic Fermat's Last Theorem holds for imaginary quadratic fields $\mathbb{Q}(\sqrt{-d})$ with $-d \equiv 2, 3 \pmod{4}$. 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. This is joint work with Samir Siksek.
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