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arXiv · 2507.16883

On Fermat's Last Theorem over the $\mathbb{Z}_3$-extension of $\mathbb{Q}$ and other fields

Luis Dieulefait·Franco Golfieri Madriaga
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Abstract

The main result of the present article is a proof of Fermat's Last Theorem for sufficiently large prime exponents $p$ with $p \equiv 2 \pmod{3}$ over certain number fields. A particular case of these fields are the maximal real subfields of the cyclotomic extensions $\mathbb{Q}(\zeta_{3^n})$ for every $n$. Our strategy consists in combining the modular method with a generalization of an arithmetic result of Pomey to these fields.

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Luis Dieulefait, Franco Golfieri Madriaga. 2025-07-22. On Fermat's Last Theorem over the $\mathbb{Z}_3$-extension of $\mathbb{Q}$ and other fields. https://arxiv.org/abs/2507.16883

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