Non-connective K-theory via universal invariants

DOI10.1112/S0010437X11005380zbMath1247.19001arXiv0903.3717MaRDI QIDQ5199365

Denis-Charles Cisinski, Gonçalo Tabuada

Publication date: 16 August 2011

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.3717

zbMATH Keywords

higher Chern charactersdg categoriesGrothendieck derivatorsnon-connective \(K\)-theory

Mathematics Subject Classification ID

(K)-theory and homology; cyclic homology and cohomology (19D55) Negative (K)-theory, NK and Nil (19D35)

Related Items (23)

Symmetric monoidal structure on non-commutative motives ⋮ Products, multiplicative Chern characters, and finite coefficients via noncommutative motives ⋮ Motivic realizations of singularity categories and vanishing cycles ⋮ Higher homotopy categories, higher derivators, and K-theory ⋮ Voevodsky's mixed motives versus Kontsevich's noncommutative mixed motives ⋮ \(\mathbf{A}^1\)-homotopy theory of noncommutative motives ⋮ Generalized non-commutative degeneration conjecture ⋮ \(t\)-structures on stable derivators and Grothendieck hearts ⋮ Parabolic semi-orthogonal decompositions and Kummer flat invariants of log schemes ⋮ Noncommutative Artin motives ⋮ Categorical smooth compactifications and generalized Hodge-to-de Rham degeneration ⋮ A universal characterization of higher algebraic \(K\)-theory ⋮ Universal suspension via noncommutative motives ⋮ Tensor triangular geometry of non-commutative motives ⋮ \(K\)-theory and the bridge from motives to noncommutative motives ⋮ Witt vectors and \(K\)-theory of automorphisms via noncommutative motives ⋮ Topological K-theory of complex noncommutative spaces ⋮ Higher symmetries in abstract stable homotopy theories ⋮ Motivic and \(\ell\)-adic realizations of the category of singularities of the zero locus of a global section of a vector bundle ⋮ Cohomological methods in intersection theory ⋮ Transfer maps and projection formulas ⋮ Bivariant cyclic cohomology and Connes' bilinear pairings in noncommutative motives ⋮ Abstract representation theory of Dynkin quivers of type \(A\)

Cites Work

• Stable homotopy theories and stabilization
• On the \(K_{-i}\)-functors
• The homotopy theory of dg-categories and derived Morita theory
• Higher \(K\)-theory via universal invariants
• About Quillen's homotopy theorie of derivatives
• Generalized spectral categories, topological Hochschild homology and trace maps
• DG quotients of DG categories.
• Cohomological direct images in model categories
• \(K\)-theory and derived equivalences
• Additivity for derivator \(K\)-theory
• Negative \(K\)-theory of derived categories
• Catégories dérivables
• Invariance de laK-Théorie par équivalences dérivées
• Homotopy theory of well-generated algebraic triangulated categories
• Moduli of objects in dg-categories
• Idempotent completion of triangulated categories

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