nLab
semiseparated scheme

A cover ${U_{i}}_{i \in I}$ of a scheme by affine open subsets is semiseparated if $U_{i} \cap U_{j}$ is also affine for every pair $(i, j) \in I \times I$ . An algebraic scheme is semiseparated if it has an affine cover which is semiseparated. The notion is introduced in