Vanishing of Nil-terms and negative <i>K</i>-theory for additive categories

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.