Let $K$ be a $p$-adic field and $L$ be a finite or infinite extension (maybe algebraic ?) of $\mathbb{Q}_p$.

Is there a reference for $p$-Hodge theory for representations $\rho : Gal_K \rightarrow GL_V(L)$ ?

In particular:

Is $Rep_L(Gal_K)$ classified by $Mod_{L \otimes_{\mathbb{Q}_p} \mathcal{E}}(\phi,\Gamma)$?

What is the definitions of 'de Rham representations' and 'Hodge-Tate weights'?