A counterexample to vanishing conjectures for negative -theory
arXiv:2006.16536 · doi:10.1007/s00222-021-01034-4
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.
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