Non connective K-theory via universal invariants

Abstract

In this article, we further the study of higher K-theory of dg categories via universal invariants, initiated by the second named author. Our main result is the co-representability of non-connective K-theory by the base ring in the universal localizing motivator. As an application, we obtain for free higher Chern characters, resp. higher trace maps, e.g. from non-connective K-theory to cyclic homology, resp. to topological Hochschild homology.

This is a slight revision in the exposition of the paper previously entitled "Negative K-theory via universal invariants"; hopefully for the best

References in corpus (2)

• Localization theorems in topological Hochschild homology and topological cyclic homology
• Topological Hochschild and cyclic homology for Differential graded categories

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• Abstract representation theory of Dynkin quivers of type A
• Accessibility and presentability in 2-categories
• Derived categories of (one-sided) exact categories and their localizations
• The fundamental theorem via derived Morita invariance, localization, and A^1-homotopy invariance
• Noncommutative Artin motives
• Non-connective K- and Nil-spectra of additive categorie
• Homotopy invariance of higher K-theory for abelian categories
• Higher K-theory of polynomial categories
• A universal characterization of noncommutative motives and secondary algebraic K-theory
• Nisnevich Descent for Deligne-Mumford Stacks
• Enriched Derivators