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

### Vladimir Sosnilo

Laboratory of Modern Algebra and Applications, Saint Petersburg State University, 14th Line V.O., 29B, Saint Petersburg 199178, Russia and St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, Fontanka, 27, Saint Petersburg 191011, Russia

## Abstract

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 $n \le 0$.

## Cite this article

Vladimir Sosnilo, Theorem of the Heart in Negative K-Theory for Weight Structures. Doc. Math. 24 (2019), pp. 2137–2158

DOI 10.4171/DM/722