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arXiv · 2501.03644

Finite length for unramified $\mathrm{GL}_2$

Christophe Breuil·Florian Herzig·Yongquan Hu·Stefano Morra·Benjamin Schraen
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Abstract

Let $p$ be a prime number and $K$ a finite unramified extension of $\mathbb{Q}_p$. If $p$ is large enough with respect to $[K:\mathbb{Q}_p]$ and under mild genericity assumptions, we prove that the admissible smooth representations of $\mathrm{GL}_2(K)$ that occur in Hecke eigenspaces of the mod $p$ cohomology are of finite length. We also prove many new structural results about these representations of $\mathrm{GL}_2(K)$ and their subquotients.

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Christophe Breuil, Florian Herzig, Yongquan Hu, Stefano Morra, Benjamin Schraen. 2025-01-07. Finite length for unramified $\mathrm{GL}_2$. https://arxiv.org/abs/2501.03644

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