locally algebraic scheme

A scheme over a field $k$ is called *locally algebraic scheme* if it has a covering $\{X_i\}$ of (open affine sub functors which are) affine schemes and all $O(X_i)$ are finitely generated $k$-algebras, i.e. if it is locally of finite type over $Spec k$.

A scheme is called *algebraic scheme* if moreover there exist a finite such covering, i.e. if it is of finite type over $Spec k$.

category: algebraic geometry

Revised on March 6, 2013 19:23:27
by Zoran Škoda
(161.53.130.104)