Integral $p$-adic Hodge theory in the imperfect residue field case

Hui Gao

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arXiv · 2007.06879

Integral $p$-adic Hodge theory in the imperfect residue field case

Hui Gao

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Abstract

Let $K$ be a mixed characteristic complete discrete valuation field with residue field admitting a finite $p$-basis, and let $G_K$ be the Galois group. We first classify semi-stable representations of $G_K$ by weakly admissible filtered $(\varphi,N)$-modules with connections. We then construct a fully faithful functor from the category of \emph{integral} semi-stable representations of $G_K$ to the category of Breuil-Kisin $G_K$-modules. Using the integral theory, we classify $p$-divisible groups over the ring of integers of $K$ by minuscule Breuil-Kisin modules with connections.

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Hui Gao. 2020-07-14. Integral $p$-adic Hodge theory in the imperfect residue field case. https://arxiv.org/abs/2007.06879

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