2 problems

Let $\rho_p:G_{\mathbb{Q}_p}\rightarrow\operatorname{GL}_2(E)$ be a continuous de Rham Galois representation, and let $B(\rho_p)$ denote the associated $p$-adic local Langlands rep…

Primitive-character cohomology conjecture. As a virtual module for $\operatorname{Gal}(\overline{\mathbf F}_q/{\mathbf F}_{q^h})$, one has $\dim\mathcal{H}_\psi=(-1)^{h-1}$, and th…