Flat Base Change Research Articles

Minimal Injective Resolutions Under Flat Base Change

For a flat morphism $\varphi :A \to B$ of noetherian rings, the minimal injective resolution of the B-module $M{ \otimes _A}B$ is described in terms of the minimal injective resolution of the finitely generated A-module M and the minimal injective resolutions of the fibers of $\varphi$.

Minimal injective resolutions under flat base change

For a flat morphism φ : A → B \varphi :A \to B of noetherian rings, the minimal injective resolution of the B-module M ⊗ A B M{ \otimes _A}B is described in terms of the minimal injective resolution of the finitely generated A-module M and the minimal injective resolutions of the fibers of φ \varphi .