Lubin–Tate theory and overconvergent Hilbert modular forms of low weight

Let K be a finite extension of ℚp and let Γ the Galois group cyclotomic K. Fontaine’s theory gives classification p-adic representations Ga( $$\overline /K$$ ) in terms (φ, Γ)-modules. A useful aspect this is Berger’s dictionary which expresses invariants coming from Hodge these In article, we use locally analytic vectors to generalize setting where Lubin—Tate As an application, show that if F totally real number field v place lying above p, then representation Gal( $${\overline _v}/{F_v}$$ associated slope overconvergent Hilbert eigenform Fv-analytic up twist trianguline. Furthermore, determine triangulation Hecke eigenvalue at v. This generalizes results case = ℚ obtained previously by Chenevier, Colmez Kisin.