Quasi-coherent sheaf

Summary

A quasi-coherent sheaf on a scheme is a sheaf of modules that is locally given by a module over the coordinate ring. On an affine scheme $\operatorname{Spec} A$, quasi-coherent sheaves are the same as $A$-modules. They form the basic category of linear objects on a scheme, closed under kernels, cokernels, direct sums and tensor products.