Definition:Scheme

Definition
Let $\struct {X, \OO_X}$ be a locally ringed space.

Let $\struct {X, \OO_X}$ be such that:
 * every point $x \in X$ has an open neighborhood $U_x$ such that:
 * the restriction of $\struct {X, \OO_X}$ to $U_x$ is an affine scheme.

Then $\struct {X, \OO_X}$ is called a scheme.

Also known as
A scheme can also be referred to as a commutative scheme.

Also see

 * Definition:Scheme over Ring
 * Definition:Separated Scheme
 * Definition:Algebraic Variety
 * Definition:Non-Commutative Scheme