Deformations of $G$-valued pseudocharacters
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911554455207936 |
|---|---|
| author | Quast, Julian |
| author_facet | Quast, Julian |
| contents | We define a deformation space of V. Lafforgue's $G$-valued pseudocharacters of a profinite group $Γ$ for a possibly disconnected reductive group $G$. We show, that this definition generalizes Chenevier's construction. We show that the universal pseudodeformation ring is noetherian and that the functor of continuous $G$-pseudocharacters on affinoid $\mathbb{Q}_p$-algebras is represented by a quasi-Stein rigid analytic space, whenever $Γ$ is topologically finitely generated. We also show that the pseudodeformation ring is noetherian, when $Γ$ satisfies Mazur's condition $Φ_p$ and $G$ satisfies a certain invariant-theoretic condition. For $G = \mathrm{Sp}_{2n}$ we describe three types of obstructed loci in the special fiber of the universal pseudodeformation space of an arbitrary residual pseudocharacter and give upper bounds for their dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14886 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Deformations of $G$-valued pseudocharacters Quast, Julian Number Theory Representation Theory 20C99 (Primary) 20G25, 11S25 (Secondary) We define a deformation space of V. Lafforgue's $G$-valued pseudocharacters of a profinite group $Γ$ for a possibly disconnected reductive group $G$. We show, that this definition generalizes Chenevier's construction. We show that the universal pseudodeformation ring is noetherian and that the functor of continuous $G$-pseudocharacters on affinoid $\mathbb{Q}_p$-algebras is represented by a quasi-Stein rigid analytic space, whenever $Γ$ is topologically finitely generated. We also show that the pseudodeformation ring is noetherian, when $Γ$ satisfies Mazur's condition $Φ_p$ and $G$ satisfies a certain invariant-theoretic condition. For $G = \mathrm{Sp}_{2n}$ we describe three types of obstructed loci in the special fiber of the universal pseudodeformation space of an arbitrary residual pseudocharacter and give upper bounds for their dimension. |
| title | Deformations of $G$-valued pseudocharacters |
| topic | Number Theory Representation Theory 20C99 (Primary) 20G25, 11S25 (Secondary) |
| url | https://arxiv.org/abs/2310.14886 |