High Quality Content by WIKIPEDIA articles! In algebraic geometry, devissage is a technique introduced by Alexander Grothendieck for proving statements about coherent sheaves on noetherian schemes. Devissage is an adaptation of a certain kind of noetherian induction. It has many applications, including the proof of generic flatness and the proof that higher direct images of coherent sheaves under proper morphisms are coherent. Laurent Gruson and Michel Raynaud extended this concept to the relative situation, that is, to the situation where the scheme under consideration is not necessarily noetherian, but instead admits a finitely presented morphism to another scheme.

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