Finite morphism

In algebraic geometry, a morphism f: X → Y of schemes is a finite morphism if Y has an open cover by affine schemes

such that for each i,

is an open affine subscheme Spec A_i, and the restriction of f to U_i, which induces a ring homomorphism

makes A_i a finitely generated module over B_i. One also says that X is finite over Y.

单词	Finite morphism
释义	Finite morphism 英语百科 Finite morphism In algebraic geometry, a morphism f: X → Y of schemes is a finite morphism if Y has an open cover by affine schemes such that for each i, is an open affine subscheme Spec A_i, and the restriction of f to U_i, which induces a ring homomorphism makes A_i a finitely generated module over B_i. One also says that X is finite over Y.
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