Quasi-coherent modules on quasi-affine schemes (Q1104363)

The paper generalizes some results of \textit{P.-J. Cahen} [Trans. Am. Math. Soc. 184 (1973), 73-85 (1974; Zbl 0276.13014)] on commutative Noetherian rings to the non-Noetherian case. Let A be a commutative ring and U a quasicompact open set. It is shown that every quasicoherent \({\mathcal O}_ U\)-module F can be represented as \(\tilde M| U\) for some A-module M. Moreover the category of quasicoherent \({\mathcal O}_ U\)-modules is equivalent to the full subcategory of A-modules M such that the natural homomorphism \(M\to Q_ U(M)\) is an isomorphism. The proof uses torsion theoretic methods.