The Stacks project

Definition 34.5.5. Let $T$ be an affine scheme. A standard smooth covering of $T$ is a family $\{ f_ j : U_ j \to T\} _{j = 1, \ldots , m}$ with each $U_ j$ is affine, $U_ j \to T$ standard smooth and $T = \bigcup f_ j(U_ j)$.