The p-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings
By Gaëtan Chenevier. 2008
134 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3709a7362acc2d39b6f54d23ba97e8005e1a1c15
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
In Mathematical Physics
- Akshay Venkatesh
- Peter Scholze
- James Newton
- Frank Calegari
- J. Thorne
- Kiran S. Kedlaya
- T. Gee
- Ruochuan Liu
Citations in the corpus
- A torsion Jacquet--Langlands correspondence (2012, background): “(For more general representations, there will presumably be a formulation of this conjecture in the language of determinants [26]).”
- Symmetric power functoriality for holomorphic modular forms, II (2020, background): “Let t = det Sym(r|GK) and t′ = det Sym(r′|GK) denote the group determinants over O (in the sense of [Che14]) associated to these two symmetric power representations, and let t denote the group determinant over k which is their common reduction modulo .”
- On torsion in the cohomology of locally symmetric varieties (2013, methodology): “Recall Chenevier’s notion of a determinant, [20], which we use as a strengthening of the notion of pseudorepresentations as introduced by Taylor, [59].”