Représentations p -adiques surconvergentes

Iwasawa theory of de Rham -modules over the Robba ring

“…By the results of Fontaine [13], Cherbonnier and Colmez [8] and Kedlaya [22], the category of p-adic representations of G K is naturally embedded in the category of (ϕ, Γ K )-modules over the Robba ring B † rig,K . The (ϕ, Γ )-modules corresponding to p-adic representations are calledétale (ϕ, Γ )-modules.…”

New methods for $$(\varphi, \Gamma)$$ ( φ , Γ ) -modules

“…The original description of this form was given by Fontaine [9] in terms of a Cohen ring for a field of formal power series, and is an easy consequence of Theorem 0.0.1. Our main focus is the refinement of Fontaine's result by Cherbonnier and Colmez [5], in which the Cohen ring is replaced with a somewhat smaller ring of convergent power series (see Theorem 2.6.2 for the precise statement). This refinement is critical to a number of applications of p-adic Hodge theory, notably Colmez's construction of the p-adic Langlands correspondence for GL 2 (Q p ) [7].…”

“…However, one can express the proof in such a way that one makes essentially the same calculations on (ϕ, Ŵ)-modules as in [5], but without any need to introduce the Tate-Sen formalism. Besides making the proof more transparent, this approach gives rise to analogous results for representations of the étale fundamental groups of some rigid analytic spaces; for instance, the theory of overconvergent relative (ϕ, Ŵ)-modules introduced by Andreatta and Brinon [1] is generalized in [19] using this approach.…”

Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality

“…Cherbonnier and Colmez [CC98] then showed, in a difficult piece of work, that D(ρ) arises via base change from a module D † (ρ) defined over the subring…”