Eigenvarieties over CM fields and trianguline representations

Eigenvarieties are parameter spaces of certain p-adic automorphic forms of varying weights. Part of the p-adic Langlands program aims to relate eigenvarieties to spaces of trianguline Galois representations. For definite unitary groups, this connection has been developed extensively, and has seen impressive applications to the Fontaine--Mazur conjecture. Our goal is to consider p-adic automorphic forms without self-duality conditions. Namely, we prove that many eigenvarieties for the group GL_n over a CM field have associated Galois representations which are trianguline. Our proof strategy is to realize such eigenvarieties inside a single eigenvariety for a unitary group, which might be of independent interest.