Let be a finite field extension of and let be its absolute Galois group. We construct the universal family of filtered -modules, or (more generally) the universal family of -modules with a Hodge–Pink lattice, and study its geometric properties. Building on this, we construct the universal family of semistable -representations in -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 in the sense of Huber. This has conjectural applications to the -adic local Langlands program.
"The universal family of semistable $p$-adic Galois representations." Algebra Number Theory 14 (5) 1055 - 1121, 2020. https://doi.org/10.2140/ant.2020.14.1055