Journal of K-theory: K-theory and its Applications to Algebra, Geometry, and Topology
- Journal of K-theory: K-theory and its Applications to Algebra, Geometry, and Topology / Volume 9 / Issue 03 / June 2012, pp 407-420
- Copyright © ISOPP 2011
- DOI: http://dx.doi.org/10.1017/is011004009jkt155 (About DOI), Published online: 24 May 2011
Research Article
The fundamental theorem via derived Morita invariance, localization, and 
1-homotopy invariance
Gonçalo Tabuadaa1*
a1 Departamento de Matematica, FCT-UNL, Quinta da Torre, 2829-516 Caparica, Portugal tabuada@fct.unl.pt
Abstract
We prove that every functor defined on dg categories, which is derived Morita invariant, localizing, and
1-homotopy invariant, satisfies the fundamental theorem. As an application, we recover in a unified and conceptual way, Weibel and Kassel's fundamental theorems in homotopy algebraic K-theory, and periodic cyclic homology, respectively.
(Received October 28 2010)
Key Words
- Fundamental theorem;
- A1-homotopy invariance;
- Dg categories;
- Homotopy algebraic K-theory;
- Periodic cyclic homology
Footnotes
* Research partially supported by the Clay Mathematics Institute and by the FCT-Portugal grant PTDC/MAT/098317/2008.
