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arXiv · 2412.06812

On the Fontaine-Mazur conjecture for $p=3$

Xinyao Zhang
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Abstract

In this article, we prove the remaining open cases of the Fontaine-Mazur conjecture on two-dimensional regular Galois representations over $\Gal(\overline{\Q}/\Q)$ when $p=3$, hence concluding the conjecture in the regular case for all odd primes. Our result is a sequel to Pan's work, based on some recent progress on $p$-adic Langlands correspondence, Galois deformation theory and a potential pro-modularity result.

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Xinyao Zhang. 2024-11-30. On the Fontaine-Mazur conjecture for $p=3$. https://arxiv.org/abs/2412.06812

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