On the Fontaine-Mazur conjecture for p=3

2024/11/30 by Xinyao Zhang, Zhang, Xinyao
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2412.06812

openalex publication_date 2024/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we prove the remaining open cases of the Fontaine-Mazur conjecture on two-dimensional regular Galois representations over \Gal(\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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