A counterexample to vanishing conjectures for negative $K$-theory
K-Theory and Homology
2021-08-04 v2 Algebraic Geometry
Category Theory
Abstract
In a 2006 article Schlichting conjectured that the negative {\it K--}theory of any abelian category must vanish. This conjecture was generalized in a 2019 article by Antieau, Gepner and Heller, who hypothesized that the negative {\it K--}theory of any category with a bounded {\it t--}structure must vanish. Both conjectures will be shown to be false.
Keywords
Cite
@article{arxiv.2006.16536,
title = {A counterexample to vanishing conjectures for negative $K$-theory},
author = {Amnon Neeman},
journal= {arXiv preprint arXiv:2006.16536},
year = {2021}
}
Comments
This is the final version, to appear soon in Inventiones Mathematica. There are a few improvements in response to comments on the original submission. Most importantly: the title of the article changed to be more informative