Scheme (mathematics) - O_X Modules

O_X Modules

Just as the R-modules are central in commutative algebra when studying the commutative ring R, so are the O_X-modules central in the study of the scheme X with structure sheaf O_X. (See locally ringed space for a definition of O_X-modules.) The category of O_X-modules is abelian. Of particular importance are the coherent sheaves on X, which arise from finitely generated (ordinary) modules on the affine parts of X. The category of coherent sheaves on X is also abelian.