On the $K$-extensions between Serre weights for unramified $\mathrm{GL}_3$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914470689767424 |
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| author | Wang, Yitong |
| author_facet | Wang, Yitong |
| contents | Let $p\geq5$ be a prime number. Let $L$ be a finite unramified extension of $\mathbb{Q}_p$ with ring of integers $\mathcal{O}_L$ and residue field $\mathbb{F}_q$. Given two Serre weights for $\mathrm{GL}_3(\mathbb{F}_q)$, we prove that in most cases the extensions between them for $\mathrm{GL}_3(\mathcal{O}_L)$ modulo the center coincide with their $\mathrm{GL}_3(\mathbb{F}_q)$-extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12071 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the $K$-extensions between Serre weights for unramified $\mathrm{GL}_3$ Wang, Yitong Number Theory Let $p\geq5$ be a prime number. Let $L$ be a finite unramified extension of $\mathbb{Q}_p$ with ring of integers $\mathcal{O}_L$ and residue field $\mathbb{F}_q$. Given two Serre weights for $\mathrm{GL}_3(\mathbb{F}_q)$, we prove that in most cases the extensions between them for $\mathrm{GL}_3(\mathcal{O}_L)$ modulo the center coincide with their $\mathrm{GL}_3(\mathbb{F}_q)$-extensions. |
| title | On the $K$-extensions between Serre weights for unramified $\mathrm{GL}_3$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2604.12071 |