The Stacks project

Situation 15.127.1. Here $R$ is a ring and $M$ is a finitely presented $R$-module. Denote $\Omega \subset \mathop{\mathrm{Spec}}(R)$ the set of closed points with the induced topology. For $x \in \Omega $ denote $M(x) = M/xM$ the fibre of $M$ at $x$. This is a finite dimensional vector space over the residue field $\kappa (x)$ at $x$. Given $s \in M$ we denote $s(x)$ the image of $s$ in $M(x)$.