Geodesic
Theorem of the Heart in Negative K-Theory for Weight Structures
Documenta mathematica, Tome 24 (2019), pp. 2137-2158.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 $n \le 0$.
Classification : 18E05, 18E30, 14F42
Keywords: homological algebra, stable homotopy theory, infinity-categories, K-theory, weight structures, Voevodsky motives 
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     author = {Sosnilo, Vladimir},
     title = {Theorem of the {Heart} in {Negative} {K-Theory} for {Weight} {Structures}},
     journal = {Documenta mathematica},
     pages = {2137--2158},
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     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a13/}
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Sosnilo, Vladimir. Theorem of the Heart in Negative K-Theory for Weight Structures. Documenta mathematica, Tome 24 (2019), pp. 2137-2158. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a13/