Dévissage

In algebraic geometry, dévissage is a technique introduced by Alexander Grothendieck for proving statements about coherent sheaves on noetherian schemes.

They did this by defining an object called a relative dévissage which is well-suited to certain kinds of inductive arguments.

As a consequence, they were able to simplify and generalize the results of EGA IV 11 on descent of flatness.

Let C be a subset of the objects of the category of coherent OX-modules which contains the zero sheaf and which has the property that, for any short exact sequence

Suppose that for every irreducible closed subset Y of X′, there exists a coherent sheaf G in C whose fiber at the generic point y of Y is a one-dimensional vector space over the residue field k(y).

[4] Gruson and Raynaud prove in wide generality that locally, dévissages always exist.