$p$-Adic Hodge parameters in the crystabelline representations of $\mathrm{GL}_n$

Yiwen Ding

doi:10.1007/s10240-025-00156-2

Article

$p$-Adic Hodge parameters in the crystabelline representations of $\mathrm{GL}_n$

Yiwen Ding ¹

¹Beijing International Center for Mathematical Research, Peking University, Beijing, China

Publications Mathématiques de l'IHÉS, Volume 142 (2025), pp. 1-74

Abstract

Let $K$ be a finite extension of $\mathbf {Q}_{p}$, and $\rho $ be an $n$-dimensional (non-critical generic) crystabelline representation of the absolute Galois group of $K$ of regular Hodge-Tate weights. We associate to $\rho $ an explicit locally $\mathbf {Q}_{p}$-analytic representation $\pi _{1}(\rho )$ of $\mathrm{GL}_n(K)$, which encodes some $p$-adic Hodge parameters of $\rho $. When $K=\mathbf {Q}_{p}$, it encodes the full information hence reciprocally determines $\rho $. When $\rho $ is associated to $p$-adic automorphic representations, we show under mild hypotheses that $\pi _{1}(\rho )$ is a subrepresentation of the $\mathrm{GL}_n(K)$-representation globally associated to $\rho $.

Article information
Cite this article

Received: 2024-08-20
Accepted: 2025-06-11
Online First: 2025-07-10
Published online: 2025-12-21

DOI: 10.1007/s10240-025-00156-2

Author's affiliations:

Yiwen Ding ¹

¹ Beijing International Center for Mathematical Research, Peking University, Beijing, China

Yiwen Ding. $p$-Adic Hodge parameters in the crystabelline representations of $\mathrm{GL}_n$. Publications Mathématiques de l'IHÉS, Volume 142 (2025), pp. 1-74. doi: 10.1007/s10240-025-00156-2

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     title = {$p${-Adic} {Hodge} parameters in the crystabelline representations of $\mathrm{GL}_n$},
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