English

Weight structure on noncommutative motives

K-Theory and Homology 2011-11-30 v1 Algebraic Geometry Algebraic Topology

Abstract

In this note we endow Kontsevich's category KMM of noncommutative mixed motives with a non-degenerate weight structure in the sense of Bondarko. As an application we obtain a convergent weight spectral sequence for every additive invariant (e.g. algebraic K-theory, cyclic homology, topological Hochschild homology, etc.), and a ring isomorphism between the Grothendieck ring of KMM and the Grothendieck ring of the category of noncommutative Chow motives.

Keywords

Cite

@article{arxiv.1111.6892,
  title  = {Weight structure on noncommutative motives},
  author = {Goncalo Tabuada},
  journal= {arXiv preprint arXiv:1111.6892},
  year   = {2011}
}

Comments

9 pages

R2 v1 2026-06-21T19:43:25.246Z