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The fundamental theorem via derived Morita invariance, localization, and 1-homotopy invariance

Published online by Cambridge University Press:  24 May 2011

Gonçalo Tabuada
Gonçalo Tabuada
Affiliation:
Departamento de Matematica, FCT-UNL, Quinta da Torre, 2829-516 Caparica, Portugaltabuada@fct.unl.pt
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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.

Keywords

Fundamental theoremA1-homotopy invarianceDg categoriesHomotopy algebraic K-theoryPeriodic cyclic homology
Type
Research Article
Information
Journal of K-Theory , Volume 9 , Issue 3 , June 2012 , pp. 407 - 420
Copyright
Copyright © ISOPP 2011

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