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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.

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