Reducers and K 0 with support

Abstract

Let R be a commutative noetherian ring, be a Serre subcategory of the category of finitely generated R-modules and be the category of finitely generated projective R-modules. We define invariants based on the categories of chain complexes from homologically supported in with support between 0 and n () and the K-group with support similar to the stable range in classical K-theory. We introduce a notion called a reducer which we use to express the class of a complex in terms of classes of complexes of smaller amplitude and use these to study and bound the above defined invariants by standard invariants like arithmetic rank, grade and projective dimension. We also give conditions for to be isomorphic to