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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2506.10901 |
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| _version_ | 1866917192140849152 |
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| author | Paškūnas, Vytautas Quast, Julian |
| author_facet | Paškūnas, Vytautas Quast, Julian |
| contents | We show that deformation rings $R^{\mathrm{ps}}$ of $G$-pseudocharacters of a profinite group $Γ$ are noetherian, when $Γ$ satisfies Mazur's finiteness condition. The proof proceeds by reduction to the case when $Γ$ is finitely generated, where the result was previously established by the second author. This enables us to extend our work on moduli spaces of $R^{\mathrm{ps}}$-condensed representations of a finitely generated profinite group $Γ$, to the groups satisfying Mazur's finiteness condition. We also show that the functor from rigid analytic spaces over $\mathbb{Q}_p$ to sets, which associates to a rigid space $Y$ the set of continuous $\mathcal{O}(Y)$-valued $G$-pseudocharacters of $Γ$ is representable by a quasi-Stein rigid analytic space, and we study its general properties. We expect these results to be useful, when studying global Galois representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10901 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deformations of pseudocharacters and Mazur's finiteness condition Paškūnas, Vytautas Quast, Julian Number Theory We show that deformation rings $R^{\mathrm{ps}}$ of $G$-pseudocharacters of a profinite group $Γ$ are noetherian, when $Γ$ satisfies Mazur's finiteness condition. The proof proceeds by reduction to the case when $Γ$ is finitely generated, where the result was previously established by the second author. This enables us to extend our work on moduli spaces of $R^{\mathrm{ps}}$-condensed representations of a finitely generated profinite group $Γ$, to the groups satisfying Mazur's finiteness condition. We also show that the functor from rigid analytic spaces over $\mathbb{Q}_p$ to sets, which associates to a rigid space $Y$ the set of continuous $\mathcal{O}(Y)$-valued $G$-pseudocharacters of $Γ$ is representable by a quasi-Stein rigid analytic space, and we study its general properties. We expect these results to be useful, when studying global Galois representations. |
| title | Deformations of pseudocharacters and Mazur's finiteness condition |
| topic | Number Theory |
| url | https://arxiv.org/abs/2506.10901 |