Solitons: Differential equations, symmetries, and infinite-dimensional algebras
《Solitons: Differential equations, symmetries, and infinite-dimensional algebras》 · 第 325 页 · Proposition and Definition 12.1
For a morphism of schemes $f:X\to Y$ the following assertions are equivalent. (i) There exists an open affine covering $(V_i)_i$ of $Y$ such that $f^{-1}(V_i)$ is an affine scheme for all $i$. (ii) For every open affine subscheme $V$ of $Y$ its inverse image $f^{-1}(V)$ is affine. If these properties are satisfied, $f$ is called affine or $X$ is called affine over $Y$.