Non connective K-theory via universal invariants

TL;DR

This paper advances the understanding of higher K-theory of dg categories by establishing its co-representability via universal invariants, enabling new constructions of higher Chern characters and trace maps.

Contribution

It proves the co-representability of non-connective K-theory in the universal localizing motivator, providing a foundation for deriving higher Chern characters and trace maps.

Findings

Co-representability of non-connective K-theory established

Higher Chern characters derived for free

Higher trace maps to cyclic homology and topological Hochschild homology obtained

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.