Non-connective K-theory via universal invariants
By Denis-Charles Cisinski, Gonçalo Tabuada. Compositio Mathematica, 2009
53 citations recorded by the source corpus.
Abstract 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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f95fd3ba673384c04bdf0541674790709ea7bbfe
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In Algebra and Number Theory
In Geometry and Topology
- D. Gepner
- Gonçalo Tabuada
- Andrew Justin Blumberg
- L. Cohn
- Clark Barwick
- Marc Hoyois
- A. Mathew
- T. Nikolaus
In Mathematical Physics
- D. Gepner
- Gonçalo Tabuada
- Andrew Justin Blumberg
- L. Cohn
- Clark Barwick
- A. Mathew
- Marc Hoyois
- T. Nikolaus
Citations in the corpus
- A universal characterization of higher algebraic K-theory (2010, background): “s of algebraic K-theory as a functor from small DG-categories to spectra and K0 as a functor from small spectral categories to abelian groups [44, 46, 47]; see also his joint work with D.-C. Cisinski [11, 12]. The basic outline of his approach is to successively localize the category of small DG-cat”
- A Guided Tour Through the Garden of Noncommutative Motives (2011, background): “[11]) Given a dg category A, we have natural equivalences of spectra RHom(U dg (k),U add dg (A)) ≃ K(A) RHom(U loc dg (k),U loc dg (A)) ≃ IK(A) .”