\(\mathbf{A}^1\)-homotopy theory of noncommutative motives

DOI10.4171/JNCG/210zbMath1345.14008arXiv1402.4432MaRDI QIDQ893798

Gonçalo Tabuada

Publication date: 20 November 2015

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.4432

zbMATH Keywords

algebraic \(K\)-theoryperiodic cyclic homologynoncommutative motivesnoncommutative algebraic geometry\(\mathbf{A}^1\) homotopyhomotopy Chern characters

Mathematics Subject Classification ID

Noncommutative algebraic geometry (14A22) (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Grothendieck groups, (K)-theory, etc. (16E20) (K)-theory and homology; cyclic homology and cohomology (19D55) (Equivariant) Chow groups and rings; motives (14C15) Negative (K)-theory, NK and Nil (19D35) Riemann-Roch theorems, Chern characters (19L10)

Related Items

Noncommutative mixed (Artin) motives and their motivic Hopf dg algebras, Some remarks on topological 𝐾-theory of dg categories, Descent in algebraic \(K\)-theory and a conjecture of Ausoni-Rognes, The Gysin triangle via localization and 𝐴¹-homotopy invariance, Voevodsky's mixed motives versus Kontsevich's noncommutative mixed motives, Higher traces, noncommutative motives, and the categorified Chern character, On the \(K\)-theory of pullbacks, The \(\text{K}\)-theory of perfectoid rings, \(\mathbb{A}^1\)-homotopy invariants of dg orbit categories

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