Toric scheme over a base ring
= Toric scheme over a base ring
{title2=$X_{\Sigma,A}$}
Given a dual pair of free lattices $N,M$ and a rational fan, glue $\operatorname{Spec}A[\sigma^\vee\cap M]$ over common-face charts. The monoid <rings> are <semigroup algebras>. A lattice map respecting cones gives a <toric morphism>. This construction works over a <commutative ring> $A$, including $\mathbb Z$, and also for an <infinite fan in toric geometry>.
// Target: toric-geometry.bigb