Let be a morphism of schemes. Let be the diagonal map. We say that is quasi-separated if is a quasicompact morphism.
A scheme is quasi-separated if the morphism is quasi-separated, i.e. is quasicompact. Every quasi-separated scheme is semiseparated.
Every separated morphism of schemes is quasi-separated; every monomorphism of schemes is separated hence also quasi-separated.
Revised on August 14, 2014 19:42:45