Let $Y$ be a connected smooth and proper $K$-variety and let $\omega$ be a non-zero $m$-pluricanonical form on $Y$, for some $m>0$. Let $K^{\prime}$ be a finite extension of $K$, set $Y^{\prime}=Y\times_{K}K^{\prime}$ and denote by $\omega^{\prime}$ the pullback of $\omega$ to $Y^{\prime}$. Then the skeleton $\mathrm{Sk}(Y,\omega)$ is the image of $\mathrm{Sk}(Y^{\prime},\omega^{\prime})$ under the projection morphism $\pi:(Y^{\prime})^{\mathrm{an}}\to Y^{\mathrm{an}}$.