Une interpretation modulaire de la variete trianguline

Using a patching module constructed in recent work of Caraiani, Emerton, Gee, Geraghty, Pa{v{s}}k{=u}nas and Shin we construct some kind of analogue of an eigenvariety. We can show that this patched eigenvariety agrees with a union of irreducible components of a space of trianguline Galois representations. Building on this we discuss the relation with the modularity conjectures for the crystalline case, a conjecture of Breuil on the locally analytic socle of representations occurring in completed cohomology and with a conjecture of Bellaiche and Chenevier on the complete local ring at certain points of eigenvarieties.