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

2020/07/14 by Hui Gao, Gao, Hui · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2007.06879

openalex publication_date 2020/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 (φ,N)-modules with connections. We then construct a fully faithful functor from the category of 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.

Citations

• A p-adic monodromy theorem for de Rham local systems

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