K-theoretic obstructions to bounded t-structures
成果类型：
Article
署名作者：
Antieau, Benjamin; Gepner, David; Heller, Jeremiah
署名单位：
University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University of Melbourne; University of Illinois System; University of Illinois Urbana-Champaign
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-018-00847-0
发表日期：
2019
页码：
241-300
关键词：
摘要：
Schlichting conjectured that the negative K-groups of small abelian categories vanish and proved this for noetherian abelian categories and for all abelian categories in degree -1. The main results of this paper are that K-1(E) vanishes when E is a small stable -category with a bounded t-structure and that K-n(E) vanishes for all n1 when additionally the heart of E is noetherian. It follows that Barwick's theorem of the heart holds for nonconnective K-theory spectra when the heart is noetherian. We give several applications, to non-existence results for bounded t-structures and stability conditions, to possible K-theoretic obstructions to the existence of the motivic t-structure, and to vanishing results for the negative K-groups of a large class of dg algebras and ring spectra.
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