Geodesic
Theorem of the Heart in Negative K-Theory for Weight Structures
Documenta mathematica, Tome 24 (2019), pp. 2137-2158
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We construct the strong weight complex functor for a stable infinity-category C equipped with a bounded weight structure w. Along the way we prove that C is determined by the infinity-categorical heart of w. This allows us to compare the K-theory of C and the K-theory of Hw, the classical heart of w.In particular, we prove that Kn​(C)→Kn​(Hw) are isomorphisms for n≤0.
DOI : 10.4171/dm/722
Classification : 14F42, 18E05
Mots-clés : homological algebra, K-theory, stable homotopy theory, Voevodsky motives, weight structures, infinity-categories 
@article{10_4171_dm_722,
     author = {Vladimir Sosnilo},
     title = {Theorem of the {Heart} in {Negative} {K-Theory} for {Weight} {Structures}},
     journal = {Documenta mathematica},
     pages = {2137--2158},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/722},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/722/}
}
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Vladimir Sosnilo. Theorem of the Heart in Negative K-Theory for Weight Structures. Documenta mathematica, Tome 24 (2019), pp. 2137-2158. doi: 10.4171/dm/722

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