(ϕ,Γ)-modules over noncommutative overconvergent and Robba rings
Abstract
We construct noncommutative multidimensional versions of overconvergent power series rings and Robba rings. We show that the category of étale
(φ,Γ)
-modules over certain completions of these rings are equivalent to the category of étale
(φ,Γ)
-modules over the corresponding classical overconvergent, resp. Robba rings (hence also to the category of
p
-adic Galois representations of
Q
p
). Moreover, in the case of Robba rings, the assumption of étaleness is not necessary, so there exists a notion of trianguline objects in this sense.