Solitons: Differential equations, symmetries, and infinite-dimensional algebras
《Solitons: Differential equations, symmetries, and infinite-dimensional algebras》 · 第 197 页 · Definition 7.38
The $\mathcal O_X$-module $\mathcal F$ is called flat over $Y$ at $x$ or $f$-flat at $x$ if $\mathcal F_x$ is a flat $\mathcal O_{Y,f(x)}$-module. It is called flat over $Y$ or $f$-flat if $\mathcal F$ is flat over $Y$ at all points $x\in X$. We say that $f$ is flat, or that $X$ is flat over $Y$, if $\mathcal O_X$ is flat over $Y$.