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Let G be a profinite group which is topologically finitely generated, p aprime number and d an integer. We show that the functor from rigid analyticspaces over Q_p to sets, which associates to a rigid space Y the set ofcontinuous d-dimensional pseudocharacters G -> O(Y), is representable by aquasi-Stein rigid analytic space X, and we study its general properties. Ourmain tool is a theory of "determinants" extending the one of pseudocharactersbut which works over an arbitrary base ring; an independent aim of this paperis to expose the main facts of this theory. The moduli space X is constructedas the generic fiber of the moduli formal scheme of continuous formaldeterminants on G of dimension d. As an application to number theory, thisprovides a framework to study the generic fibers of pseudodeformation rings(e.g. of Galois representations), especially in the "residually reducible"case, and including when p <= d.

The p-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings