The p-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings
Abstract
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 independent aim of this paper is to expose the main facts of this theory. The moduli space X is constructed as the generic fiber of the moduli formal scheme of continuous formal determinants on G of dimension d. As an application to number theory, this provides 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.
Keywords
Cite
@article{arxiv.0809.0415,
title = {The p-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings},
author = {Gaetan Chenevier},
journal= {arXiv preprint arXiv:0809.0415},
year = {2013}
}
Comments
56 pages. v2 : final version, to appear in the Proceedings of the LMS Durham Symposium "Automorphic forms and Galois representations" (2011)