Corollary 7.4.3 has some mistakes (inherited from the original version).
(Corollary 7.4.3). On an integral prescheme $X$, every torsion-free quasi-coherent $O_X$-module of rank 1
(in particular, every invertible $O_X$-module) is isomorphic to an $O_X$-submodule of $R(X)$, and vice versa.
The "vice versa" part has counterexamples like skyscraper sheaves.
The correct statement should be
(correct Corollary 7.4.3). On an integral prescheme $X$, every torsion-free quasi-coherent $O_X$-module of rank 1
(in particular, every invertible $O_X$-module) is isomorphic to a nonzero and quasi-coherent $O_X$-submodule of $R(X)$, and vice versa.
Corollary 7.4.3 has some mistakes (inherited from the original version).
(Corollary 7.4.3). On an integral prescheme$X$ , every torsion-free quasi-coherent $O_X$ -module of rank 1$O_X$ -module) is isomorphic to an $O_X$ -submodule of $R(X)$ , and vice versa.
(in particular, every invertible
The "vice versa" part has counterexamples like skyscraper sheaves.
The correct statement should be
(correct Corollary 7.4.3). On an integral prescheme$X$ , every torsion-free quasi-coherent $O_X$ -module of rank 1$O_X$ -module) is isomorphic to a nonzero and quasi-coherent $O_X$ -submodule of $R(X)$ , and vice versa.
(in particular, every invertible