Answer by Laurent Berger for $(\varphi, \Gamma)$-module of dimension 2 modulo...
The answer is "no" in general. If $\delta_2=1$ and $\delta_1$ is the mod $p$ cyclotomic character, then there are both peu and très ramifiées extensions. Let $res(g)$ denote the coefficient of $1/X$ in...
View Article$(\varphi, \Gamma)$-module of dimension 2 modulo $p$
Let $p$ be a prime number $\geq 3$. Let $V$ be a representation of $Gal(\bar{\mathbb{Q}}_p/ \mathbb{Q}_p)$ with coefficients in $\mathbb{F}_p$. Assume $V$ is a non-split extension of two characters...
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