Projective smooth representations in natural characteristic
| Autor: | Ophir, Amit, Sorensen, Claus |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We investigate under which circumstances there exists nonzero {\it{projective}} smooth $\field[G]$-modules, where $\field$ is a field of characteristic $p$ and $G$ is a locally pro-$p$ group. We prove the non-existence of (non-trivial) projective objects for so-called {\it{fair}} groups -- a family including $\bf{G}(\frak{F})$ for a connected reductive group $\bf{G}$ defined over a non-archimedean local field $\frak{F}$. This was proved in \cite{SS24} for finite extensions $\frak{F}/\Bbb{Q}_p$. The argument we present in this note has the benefit of being completely elementary and, perhaps more importantly, adaptable to $\frak{F}=\Bbb{F}_q(\!(t)\!)$. Finally, we elucidate the fairness condition via a criterion in the Chabauty space of $G$. Comment: 12 pages |
| Databáze: | arXiv |
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