In a 2006 article Schlichting conjectured that the negative 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 K–theory of any category with a bounded t–structure must vanish. Both conjectures will be shown to be false.
A counterexample to vanishing conjectures for negative K-theory / A. Neeman. - In: INVENTIONES MATHEMATICAE. - ISSN 0020-9910. - 225:(2021), pp. 427-452. [10.1007/s00222-021-01034-4]
A counterexample to vanishing conjectures for negative K-theory
A. Neeman
2021
Abstract
In a 2006 article Schlichting conjectured that the negative 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 K–theory of any category with a bounded t–structure must vanish. Both conjectures will be shown to be false.
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