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arXiv · 1312.6371

The universal family of semi-stable p-adic Galois representations

Urs Hartl·Eugen Hellmann
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Abstract

Let $K$ be a finite field extension of $Q_p$ and let $G_K$ be its absolute Galois group. We construct the universal family of filtered $(ϕ,N)$-modules, or (more generally) the universal family of $(ϕ,N)$-modules with a Hodge-Pink lattice, and study its geometric properties. Building on this, we construct the universal family of semi-stable $G_K$-representations in $Q_p$-algebras. All these universal families are parametrized by moduli spaces which are Artin stacks in schemes or in adic spaces locally of finite type over $Q_p$ in the sense of Huber. This has conjectural applications to the $p$-adic local Langlands program.

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Urs Hartl, Eugen Hellmann. 2020-01-16. The universal family of semi-stable p-adic Galois representations. https://doi.org/10.2140/ant.2020.14.1055

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