Theorem of the heart in negative K-theory for weight structures

2017/05/22 by Vladimir Sosnilo, Sosnilo, Vladimir · 4 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.1705.07995

Abstract

We construct the strong weight complex functor (in the sense of Bondarko) for a stable infinity-category \underlineC equipped with a bounded weight structure w. Along the way we prove that \underlineC is determined by the infinity-categorical heart of w. This allows us to compare the K-theory of \underlineC and the K-theory of \underlineHw, the classical heart of w. In particular, we prove that K_n(\underlineC) → K_n(\underlineHw) are isomorphisms for n ≤ 0.

Cited by

• On the tensor-triangular geometry of isotropic motives
• The weight filtration on real singular homology is motivic
• Weights for K-motives on stacks
• A Weight Structure on Rigid Analytic Motives over a Field

Related

• Weight structures and the algebraic K-theory of stable ∞-categories
• A Theorem of the Heart for K-theory of Endomorphisms
• Hearts and towers in stable infinity-categories
• The heart fan of an abelian category
• K-theoretic obstructions to bounded t-structures