Non-connective K-theory via universal invariants

Denis-Charles Cisinski (1) , Gonçalo Tabuada (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 FCT NOVA - Faculdade de Ciências e Tecnologia = School of Science & Technology

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, from non-connective K-theory to cyclic homology, resp. to topological Hochschild homology.

Domaines: K-théorie et homologie [math.KT]

Denis-Charles Cisinski, Gonçalo Tabuada. Non-connective K-theory via universal invariants. Compositio Mathematica, 2011, 147 (4), pp.1281-1320. ⟨10.1112/S0010437X11005380⟩. ⟨hal-00440932⟩