Vanishing of Nil-terms and negative K-theory for additive categories

Abstract

We extend the notion of regular coherence from rings to additive categories and show that well-known consequences of regular coherence for rings also apply to additive categories. For instance the negative K-groups and all twisted Nil-groups vanish for an additive category if it is regular coherent. This will be applied to nested sequences of additive categories, motivated by our ongoing project to determine the algebraic K-theory of the Hecke algebra of a reductive p-adic group.

64 pages, minor revisions in Section 14

References in corpus (2)

• Split injectivity of A-theoretic assembly maps
• Shortening binary complexes and commutativity of $K$-theory with infinite products