Theorem of the Heart in Negative K-Theory for Weight Structures

Doc. Math. 24, 2137-2158 (2019)
DOI: 10.25537/dm.2019v24.2137-2158

Summary

We construct the strong weight complex functor for a stable infinity-category $\mathcal{C}$ equipped with a bounded weight structure $w$. Along the way we prove that $\mathcal{C}$ is determined by the infinity-categorical heart of $w$. This allows us to compare the K-theory of $\mathcal{C}$ and the K-theory of $Hw$, the classical heart of $w. In$ particular, we prove that $K_n(\mathcal{C}) \to K_n(Hw)$ are isomorphisms for $n \le 0$.

Mathematics Subject Classification

18E05, 18E30, 14F42

Keywords/Phrases

homological algebra, stable homotopy theory, infinity-categories, K-theory, weight structures, Voevodsky motives

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