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Non-connective K-theory via universal invariants

Part of: Homological algebra Higher algebraic $K$-theory

Published online by Cambridge University Press:  04 May 2011

Denis-Charles Cisinski  and
Gonçalo Tabuada
Denis-Charles Cisinski
Affiliation:
Université Paul Sabatier, Institut de Mathématiques de Toulouse, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France (email: [email protected])
Gonçalo Tabuada
Affiliation:
Departamento de Matemática e CMA, FCT-UNL Quinta da Torre, 2829-516 Caparica, Portugal (email: [email protected])
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Abstract

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In this article, we further the study of higher K-theory of differential graded (dg) categories via universal invariants, initiated in [G. Tabuada, Higher K-theory via universal invariants, Duke Math. J. 145 (2008), 121–206]. 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, respectively higher trace maps, from non-connective K-theory to cyclic homology, respectively to topological Hochschild homology.

Keywords

non-connective K-theorydg categorieshigher Chern charactersGrothendieck derivators

MSC classification

Secondary: 19D35: Negative $K$-theory, NK and Nil 19D55: $K$-theory and homology; cyclic homology and cohomology 18G55: Homotopical algebra
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 4 , July 2011 , pp. 1281 - 1320
Copyright
Copyright © Foundation Compositio Mathematica 2011

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