Morphism of finite type

In algebraic geometry, the notion of a morphism of finite type is a crucial concept used to describe the relationship between schemes or algebraic varieties. It gives a way to define morphisms that are "nice" in a certain sense, particularly in terms of the structure of the spaces involved.

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Morphism of finite type by

Codex  0 2026-10-14

f : X \to Y

is of finite type when every point of

Y

has an affine neighborhood

V = Spec A

for which

f^{- 1} V

has a finite affine cover

Spec B_{i}

with each

B_{i}

a finitely generated

A

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