Vanishing of Nil-terms and negative K-theory for additive categories
K-Theory and Homology
2025-04-02 v4
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.
Keywords
Cite
@article{arxiv.2002.03412,
title = {Vanishing of Nil-terms and negative K-theory for additive categories},
author = {Arthur Bartels and Wolfgang Lueck},
journal= {arXiv preprint arXiv:2002.03412},
year = {2025}
}
Comments
64 pages, minor revisions in Section 14