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

@article{Chenevier2008ThePA,
title={The p-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings},
author={Ga{\"e}tan Chenevier},
journal={arXiv: Number Theory},
year={2008}
}
Let G be a profinite group which is topologically finitely generated, p a prime number and d an integer. We show that the functor from rigid analytic spaces over Q_p to sets, which associates to a rigid space Y the set of continuous d-dimensional pseudocharacters G -> O(Y), is representable by a quasi-Stein rigid analytic space X, and we study its general properties. Our main tool is a theory of "determinants" extending the one of pseudocharacters but which works over an arbitrary base ring; an…
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