Localization of A Module - (Quasi-)coherent Sheaves

(Quasi-)coherent Sheaves

In terms of localization of modules, one can define quasi-coherent sheaves and coherent sheaves on locally ringed spaces. In algebraic geometry, the quasi-coherent O_X-modules for schemes X are those that are locally modelled on sheaves on Spec(R) of localizations of any R-module M. A coherent O_X-module is such a sheaf, locally modelled on a finitely-presented module over R.