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

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 $(\varphi ,N)$-modules, or (more generally) the universal family of $(\varphi ,N)$-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.

final version, to appear in ANT

References in corpus (5)

• Slope filtrations for relative Frobenius
• A local model for the trianguline variety and applications
• Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings
• The p-adic local Langlands correspondence for GL_2(Q_p)
• Phi-modules and coefficient spaces

Cited by in corpus (4)

• Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings
• On the Breuil-Schneider conjecture: Generic case
• Generic smoothness for $G$-valued potentially semi-stable deformation rings
• Companion points on the eigenvariety with non-regular weights