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arXiv · 2404.00389

On the rank of the multivariable $(\varphi,\mathcal{O}_K^{\times})$-modules associated to mod $p$ representations of $\operatorname{GL}_2(K)$

Yitong Wang
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Abstract

Let $p$ be a prime number, $K$ a finite unramified extension of $\mathbb{Q}_p$ and $\mathbb{F}$ a finite extension of $\mathbb{F}_p$. For $\pi$ an admissible smooth representation of $\operatorname{GL}_2(K)$ over $\mathbb{F}$ satisfying certain multiplicity-one properties, we compute the rank of the associated \'etale $(\varphi,\mathcal{O}_K^{\times})$-module $D_A(\pi)$ defined by Breuil-Herzig-Hu-Morra-Schraen, extending their results.

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Yitong Wang. 2024-03-30. On the rank of the multivariable $(\varphi,\mathcal{O}_K^{\times})$-modules associated to mod $p$ representations of $\operatorname{GL}_2(K)$. https://arxiv.org/abs/2404.00389

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