III.1.1 Let R be a commutative ring and S a commutative R- algebra; then many properties of modules N over R are inherited by the corresponding S-module S ⊗ _R M, such as the properties of being finitely generated, free, or projective. General descent theory is concerned with the inverse question: how to “descend” properties over S to properties over R. In particular, when does an element, a module, an algebra over S “come from” a similar object over R?