(2.1.6) We will use the following notations from [MN13]. If $\mathscr{X}$ is a normal model of $X$ over $\mathscr{C}$, $x$ is a point of $\widehat{\mathscr{X}}_{\eta}$ and $D$ is a divisor on $\mathscr{X}$ that is supported on $\mathscr{X}_{s}$ and Cartier at $\mathrm{red}_{\mathscr{X}}(x)$, then we set

$$v_{x}(D)=-\ln|f(x)|$$

where $f$ is any element of the local ring of $\mathscr{X}$ at $\mathrm{red}_{\mathscr{X}}(x)$ such that $D=\mathrm{div}(f)$ locally at $\mathrm{red}_{\mathscr{X}}(x)$. It is clear that $v_{x}(D)$ is linear in $D$. If $\mathscr{X}$ is regular and $\omega$ is a non-zero rational section of $\omega_{\mathscr{X}_{R}/R}^{\otimes m}$, for some $m>0$ (for instance, an $m$-pluricanonical form on $X_{K}$) then we denote by $\mathrm{div}_{\mathscr{X}}(\omega)$ the corresponding divisor on $\mathscr{X}_{R}$.