Christophe Breuil, Florian Herzig, Yongquan Hu, Stefano Morra, Benjamin Schraen
Published 2025-01-07Version 1
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.
On the rank of the multivariable $(\varphi,\mathcal{O}_K^{\times})$-modules associated to mod $p$ representations of $\operatorname{GL}_2(K)$
Comparison of algorithms to calculate quadratic irregularity of prime numbers
Several new relations for the $n^{th}$ prime number
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