Let $L$ be an ample line bundle on the projective variety $X$ over $K$ and let ${\mathscr{X}}_{0}$ be any ${K^{\circ}}$-model of $X$. Then there is a ${K^{\circ}}$-model ${\mathscr{X}}$ of $X$ dominating ${\mathscr{X}}_{0}$ and an ample line bundle ${\mathscr{L}}$ on ${\mathscr{X}}$ which is a ${K^{\circ}}$-model of $L^{\otimes m}$ for a suitable $m\in{\mathbb{N}}$.