ON SOME PROPERTY OF -ADIC FAMILIES OF POTENTIALLY SEMI-STABLE REPRESENTATIONS
ON SOME PROPERTY OF -ADIC FAMILIES OF POTENTIALLY SEMI-STABLE REPRESENTATIONS
Let $p$ be an odd prime number and $\left\{\rho_k\right\}_{k \in \mathcal{K}}$ be a $p$-adic analytic family of potentially semi-stable representations $\rho_k$ with an arithmetic progression $\mathcal{K}$. Under some assumptions, we shall prove in this article that if there exists some $k \in \mathcal{K}$ such that the $W_{\mathbb{Q}_p}$ representation $D_{\mathrm{pst}}\left(\rho_k\right)$ associated …