A toric scheme over $S$ of relative dimension $n$ is a normal integral separated $S$-scheme of finite type, ${\mathcal{X}}$, equipped with a dense open embedding $\mathbb{T}_{K}\hookrightarrow{\mathcal{X}}_{\eta}$ and an $S$-action of $\mathbb{T}_{S}$ over ${\mathcal{X}}$ that extends the action of $\mathbb{T}_{K}$ on itself by translations. If we want to stress the torus acting on ${\mathcal{X}}$ we will call them toric schemes with torus $\mathbb{T}_{S}$.