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arXiv · 1510.07503

Kisin modules with descent data and parahoric local models

Ana Caraiani·Brandon Levin
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Abstract

We construct a moduli space $Y^{μ, τ}$ of Kisin modules with tame descent datum $τ$ and with fixed $p$-adic Hodge type $\leq μ$, for some finite extension $K/\mathbb{Q}_p$. We show that this space is smoothly equivalent to the local model for $\mathrm{Res}_{K/\mathbb{Q}_p} \mathrm{GL}_n$, cocharacter $\{ μ\}$, and parahoric level structure. We use this to construct the analogue of Kottwitz-Rapoport strata on the special fiber $Y^{μ, τ}$ indexed by the $μ$-admissible set. We also relate $Y^{μ, τ}$ to potentially crystalline Galois deformation rings.

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Ana Caraiani, Brandon Levin. 2018-01-11. Kisin modules with descent data and parahoric local models. https://arxiv.org/abs/1510.07503

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