On the Fontaine-Mazur conjecture for $p=3$
Number Theory
2025-07-23 v4
Abstract
In this article, we prove the remaining open cases of the Fontaine-Mazur conjecture on two-dimensional regular Galois representations over when , 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 -adic Langlands correspondence, Galois deformation theory and a potential pro-modularity result.
Cite
@article{arxiv.2412.06812,
title = {On the Fontaine-Mazur conjecture for $p=3$},
author = {Xinyao Zhang},
journal= {arXiv preprint arXiv:2412.06812},
year = {2025}
}
Comments
54 pages. arXiv admin note: substantial text overlap with arXiv:1901.07166, arXiv:1005.2008 by other authors