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arXiv · 2604.12071

On the $K$-extensions between Serre weights for unramified $\mathrm{GL}_3$

Yitong Wang
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Abstract

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.

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Yitong Wang. 2026-04-13. On the $K$-extensions between Serre weights for unramified $\mathrm{GL}_3$. https://arxiv.org/abs/2604.12071

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