 Sheaf of modules

For a ringed space $(X,{\mathcal{O}}_X)$, a sheaf of ${\mathcal{O}}_X$-modules is a sheaf $\mathcal{F}$ such that every $\mathcal{F}(U)$ is an ${\mathcal{O}}_X(U)$-module and restriction maps preserve scalar multiplication.

A sheaf of modules is a fundamental concept in both algebraic geometry and sheaf theory, combining the ideas of sheaves and modules. Let's break this down: ### Sheaves A **sheaf** on a topological space \( X \) is a tool for systematically tracking local data attached to the open sets of \( X \).