$\sigma$ de Rham p-adic Galois representations In the paper of Liang Xiao. Tensor being crystalline implies each factor being crystalline up to twist, the author says that a $G_K$ representation $\rho$ is de Rham if and only if $\rho$ is $\sigma$-de Rham for all $\sigma\in Gal(K/Q_p)$ in the proof of theorem 1, where $K$ is a finite Galois extension of $Q_p$. I don't know how to prove this. Thanks for any answers.

$V \otimes_{\mathbf{Q}_p} B_{dR} = \bigoplus_\sigma \left( V \otimes_{K, \sigma} B_{dR}\right)$.