  We construct and study the moduli of continuous representations of a
profinite group with integral $p$-adic coefficients. We present this moduli
space over the moduli space of continuous pseudorepresentations and show that
this morphism is algebraizable. When this profinite group is the absolute
Galois group of a $p$-adic local field, we show that these moduli spaces admit
Zariski-closed loci cutting out Galois representations that are potentially
semi-stable with bounded Hodge-Tate weights and a given Hodge and Galois type.
As a consequence, we show that these loci descend to the universal deformation
ring of the corresponding pseudorepresentation.
