nLab
open subscheme

An open subscheme of a scheme $(Y,{𝒪}_Y)$ is a scheme $(U,{𝒪}_Y)$ whose underlying space is the subspace $U$ of $Y$ together with an isomorphism of the structure sheaf ${𝒪}_U$ with the restriction ${𝒪}_Y{\mid }_U$ of the structure sheaf ${𝒪}_Y$ to $U$. An isomorphism of a scheme $(X,{𝒪}_X)$ and an open subscheme $(U,{𝒪}_Y)$ of another scheme $(Y,{𝒪}_Y)$ amounts to an open immersion of schemes $(X,{𝒪}_X)\hookrightarrow (Y,{𝒪}_Y)$.

category: algebraic geometry