Sosnilo, Vladimir

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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Affiliation

Sosnilo, Vladimir
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, Russi

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