On some partially de Rham Galois representations

Abstract

We study some partially de Rham representations of $\mathrm{Gal}(\bar{L}/L)$ for a finite unramified extension $L$ of ${\mathbb{Q}}_p$. We study some related subspaces of Galois cohomology and of cohomology of $B$-pairs. As an application, we associate a locally ${\mathbb{Q}}_p$-analytic representation of ${\mathrm{GL}}_2(L)$ to a $2$-dimensional trianguline representation of $\mathrm{Gal}(\bar{L}/L)$, by generalizing Breuil's theory in the crystalline case.

This paper has been withdrawn by the author, the result "partial non-critialness implies partial de Rhamness" has been merged into arXiv:1508.07420

Cited by in corpus (1)

• $\mathcal{L}$-invariants and local-global compatibility for the group ${\mathrm{GL}}_2/F$