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Potential semistability of Finite height Galois representations: Relative case
Let $K$ be a $p$-adic field. We define the notion of finite height for an étale $\mathbb{Z}_p$-local system on a smooth affinoid adic space $\mathcal{X}$ over $K$ with semistable reduction. Using analytic prismatic $F$-crystals and purity results of Du-Liu-Moon-Shimizu (arXiv:2404.19603), we prove t
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