nLab locally algebraic scheme

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

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

Last revised on March 6, 2013 at 19:23:27. See the history of this page for a list of all contributions to it.