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Let $K$ be a finite extension of $\mathbb{Q}_p$, and let $\overline{\rho}:\mathrm{Gal}(\overline{K}/K)\rightarrow \mathrm{GL}_2(\mathbb{F})$ be a characteristic $p$ representation. According to a ...

Notation: $K$ finite extension of $\mathbb{Q}_p$, $G_K$ absolute Galois group of $K$, $E$ is finite extension of $\mathbb{Q}_p$ (coefficient field), $O_E$ is ring of integer in $E$. In this paper of ...