Let $R$ be a ring with unity, and $X = \mathrm{Spec}\, R$ be its prime spectrum. Given an $R$ -module $M$ , one can define a presheaf on $X$ by defining its sections on an open set $U$ to be $\O_X(U)\otimes_R M$ . We call the sheafification of this $\tilde M$ , and a sheaf of this form on $X$ is called quasi-coherent. If $M$ is a finitely generated module, then $\tilde{M}$ is called coherent. A sheaf on an arbitrary scheme $X$ is called (quasi-)coherent if it is (quasi-)coherent on each open affine subset of $X$ .