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arXiv · 1811.10260

Inertial and Hodge--Tate weights of crystalline representations

Robin Bartlett
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Abstract

Let $K$ be an unramified extension of $\mathbb{Q}_p$ and $\rho\colon G_K \rightarrow \operatorname{GL}_n(\overline{\mathbb{Z}}_p)$ a crystalline representation. If the Hodge--Tate weights of $\rho$ differ by at most $p$ then we show that these weights are contained in a natural collection of weights depending only on the restriction to inertia of $\overline{\rho} = \rho \otimes_{\overline{\mathbb{Z}}_p} \overline{\mathbb{F}}_p$. Our methods involve the study of a full subcategory of $p$-torsion Breuil--Kisin modules which we view as extending Fontaine--Laffaille theory to filtrations of length $p$.

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Robin Bartlett. 2018-11-26. Inertial and Hodge--Tate weights of crystalline representations. https://arxiv.org/abs/1811.10260

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