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arXiv · 2601.20395

Remarks on the Boston Unramified Fontaine-Mazur Conjecture, II

Yufan Luo
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Abstract

In this paper, we investigate Boston's generalization of the unramified Fontaine-Mazur conjecture for Galois representations. From a group-theoretic perspective, we first show that the conjecture can be reduced to the case of certain distinguished classes of $p$-adic analytic groups and $\mathbb{F}_{p}[[T]]$-adic analytic groups. Specifically, these are open subgroups of the groups of integral points of absolutely simple algebraic groups defined over non-Archimedean local fields. Furthermore, we provide a group-theoretic interpretation of the conjecture in terms of the virtually Golod-Shafarevich property. Finally, we establish a local-global principle and a prime-to-adjoint principle for the conjecture.

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Yufan Luo. 2026-01-28. Remarks on the Boston Unramified Fontaine-Mazur Conjecture, II. https://arxiv.org/abs/2601.20395

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