Mod $p$ Iwasawa algebras of pro-$p$ Iwahori subgroups
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908763497168896 |
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| author | Ariaz, Rudy Creech, Steven Hu, Bryan Khunger, Simran Koziol, Karol Rankothge, Bharatha Zhang, Bobby Zixuan |
| author_facet | Ariaz, Rudy Creech, Steven Hu, Bryan Khunger, Simran Koziol, Karol Rankothge, Bharatha Zhang, Bobby Zixuan |
| contents | Suppose $F$ is a finite unramified extension of $\mathbb{Q}_p$, and $G$ is the group of $F$-points of a split, connected, reductive group over $F$. Under a natural restriction on $p$, we determine the structure of the graded mod $p$ Iwasawa algebra $\textrm{gr}_{\mathfrak{m}}(\mathbb{F}_p [\![ I]\!])$, where $I$ is a pro-$p$ Iwahori subgroup of $G$. We also determine its maximal commutative quotient, and relate these results to Gelfand--Kirillov dimensions of smooth mod $p$ representations of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09021 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mod $p$ Iwasawa algebras of pro-$p$ Iwahori subgroups Ariaz, Rudy Creech, Steven Hu, Bryan Khunger, Simran Koziol, Karol Rankothge, Bharatha Zhang, Bobby Zixuan Representation Theory Number Theory Suppose $F$ is a finite unramified extension of $\mathbb{Q}_p$, and $G$ is the group of $F$-points of a split, connected, reductive group over $F$. Under a natural restriction on $p$, we determine the structure of the graded mod $p$ Iwasawa algebra $\textrm{gr}_{\mathfrak{m}}(\mathbb{F}_p [\![ I]\!])$, where $I$ is a pro-$p$ Iwahori subgroup of $G$. We also determine its maximal commutative quotient, and relate these results to Gelfand--Kirillov dimensions of smooth mod $p$ representations of $G$. |
| title | Mod $p$ Iwasawa algebras of pro-$p$ Iwahori subgroups |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2601.09021 |