4 problems

Let $\mathbb{G}$ be a one-dimensional formal group of finite height $n$ over a perfect field $k$ of characteristic $p$, and let $\ell$ and $p$ be distinct primes. Write $H^{n-1}$ f…

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…

The $p$-adic local Langlands correspondence associates representations of $\operatorname{GL}_2(\mathbb{Q}_p)$ with suitable two-dimensional $p$-adic Galois representations. The Lub…

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…