Definition:Scheme

Definition
A commutative scheme is a locally ringed space $(X, \mathcal O_X)$ such that every point $x \in X$ has an open neighborhood $U$ such that the restriction of $(X, \mathcal O_X)$ to $U$ is an affine commutative scheme.

Also known as
Outside noncommutative algebraic geometry this also simply called a scheme.

Also see

 * Definition:Scheme over Ring
 * Definition:Separated Scheme
 * Definition:Algebraic Variety