Solitons: Differential equations, symmetries, and infinite-dimensional algebras
《Solitons: Differential equations, symmetries, and infinite-dimensional algebras》 · 第 199 页 · Definition 7.45
Let $(X,\mathcal O_X)$ be a ringed space. An $\mathcal O_X$-module $\mathcal F$ is called coherent if $\mathcal F$ is of finite type and if for every open subset $U\subseteq X$, every integer $n\geq 0$, and for every homomorphism $w:\mathcal O_X^n|_U\to\mathcal F|_U$ the kernel of $w$ is of finite type.