morphism of finite type
A homomorphism between schemes is said to be (locally) of finite type it it behaves like a finite covering space.
A morphism of schemes is locally of finite type if
for every open cover by affine schemes, ;
and every cover by affine schemes , fitting into a commuting diagram (this always exists, see coverage)
for all ,
we have that the morphism of algebras formally dual to exhibits as a finitely generated algebra over .
If for fixed the range only over a finite set, then the morphism is said to be of finite type.
Introductory disucssoon over the complex numbers (with an eye towards GAGA) is in
- Amnon Neeman, section 3.10 Algebraic and analytic geometry, London Math. Soc. Lec. Note Series 345, 2007 (publisher)