# Quillen's Devissage in Geometry

In this talk we discuss a new perspective on Quillen's devissage theorem. Originally, Quillen proved devissage for algebraic -theory of abelian categories. The theorem showed that given a full abelian subcategory of an abelian category , if every object of has a finite filtration with quotients lying in . This allows us, for example, to relate the -theory of torsion -modules to the -theories of -modules for all . Generalizations of this theorem to more general contexts for -theory, such as Walhdausen categories, have been notoriously difficult; although some such theorems exist they are generally much more complicated to state and prove than Quillen's original. In this talk we show how to translate Quillen's algebraic approach to a geometric context. This translation allows us to construct a devissage theorem in geometry, and prove it using Quillen's original insights.