Remarks on the Boston Unramified Fontaine-Mazur Conjecture, II
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912854535307264 |
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| author | Luo, Yufan |
| author_facet | Luo, Yufan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20395 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Remarks on the Boston Unramified Fontaine-Mazur Conjecture, II Luo, Yufan Number Theory primary 11F80, secondary 20E18 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. |
| title | Remarks on the Boston Unramified Fontaine-Mazur Conjecture, II |
| topic | Number Theory primary 11F80, secondary 20E18 |
| url | https://arxiv.org/abs/2601.20395 |