%0 Journal Article
%T Une interpr¨¦tation modulaire de la vari¨¦t¨¦ trianguline
%A Christophe Breuil
%A Eugen Hellmann
%A Benjamin Schraen
%J Mathematics
%D 2014
%I arXiv
%X 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 Bella\"iche and Chenevier on the complete local ring at certain points of eigenvarieties.
%U http://arxiv.org/abs/1411.7260v2