Non-regular trianguline representations

Abstract

Let $G_{\mathbb{Q}_p}$ be the absolute Galois group of $\mathbb{Q}_p$ and let $L$ be a finite extension of $\mathbb{Q}_p$. Moreover let $\bar\rho:G_{\mathbb{Q}_p}\rightarrow GL_n(k_L)$ be a continous representation of $G_{\mathbb{Q}_p}$, where $k_L$ is the residue field of $L$ and $n$ is a natural number greater than $1$. We find sufficient conditions for which a trianguline representation $\rho:G_{\mathbb{Q}_p}\rightarrow GL_n(L)$ lifting $\bar\rho$ is a point of the trianguline variety associated to $\bar\rho$.