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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.12071 |
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Table of 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.