Finite length for unramified $\mathrm{GL}_2$
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914236934914048 |
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| author | Breuil, Christophe Herzig, Florian Hu, Yongquan Morra, Stefano Schraen, Benjamin |
| author_facet | Breuil, Christophe Herzig, Florian Hu, Yongquan Morra, Stefano Schraen, Benjamin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03644 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite length for unramified $\mathrm{GL}_2$ Breuil, Christophe Herzig, Florian Hu, Yongquan Morra, Stefano Schraen, Benjamin Number Theory Representation Theory 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. |
| title | Finite length for unramified $\mathrm{GL}_2$ |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2501.03644 |