K-theoretic obstructions to bounded t-structures
K-theoretic obstructions to bounded t-structures
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DOI：
10.1007/s00222-018-00847-0
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发表时间：
2016-10
影响因子：
3.1
通讯作者：
Benjamin Antieau;David Gepner;J. Heller
中科院分区：
文献类型：
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作者：
Benjamin Antieau;David Gepner;J. Heller
Schlichting证明了小交换范畴的负K-群为零，并对Noether交换范畴和所有交换范畴的度证明了这一点。本文的主要结果是：当E是一个具有有界dt-结构的小稳定范畴时，由此可见，当心脏是noetherian时，心脏的巴维克定理适用于非连通K理论谱。我们给出了几个应用程序，不存在的结果boundedt结构和稳定性条件，可能的K理论障碍的动机结构的存在，并消失的negativeK-群的一大类dg代数和环谱的结果。
Schlichting conjectured that the negativeK-groups of small abelian categories vanish and proved this for noetherian abelian categories and for all abelian categories in degree. The main results of this paper are thatvanishes whenEis a small stable-category with a boundedt-structure and thatvanishes for allwhen additionally the heart ofEis noetherian. It follows that Barwick’s theorem of the heart holds for nonconnectiveK-theory spectra when the heart is noetherian. We give several applications, to non-existence results for boundedt-structures and stability conditions, to possibleK-theoretic obstructions to the existence of the motivict-structure, and to vanishing results for the negativeK-groups of a large class of dg algebras and ring spectra.