Homology, Homotopy and Applications

Volume 11 (2009)

Number 2

Algebraic $K$-theory and cubical descent

Pages: 5 – 25

DOI: http://dx.doi.org/10.4310/HHA.2009.v11.n2.a2

Authors

Pere Pascual (Departament de Matemàtica Aplicada 1, Universitat Politècnica de Catalunya, Barcelona, Spain)

Llorenç Rubió Pons (Departament de Matemàtica Aplicada 1, Universitat Politècnica de Catalunya, Barcelona, Spain)

Abstract

In this note we apply the Guillén-Navarro descent theorem to define a descent variant of the algebraic $K$-theory of varieties over a field of characteristic zero, $\mathcal{K}D(X)$, which coincides with $\mathcal{K}(X)$ for smooth varieties and to prove that there is a natural weight filtration on the groups $KD-*(X)$. After a result of Haesemeyer, we deduce that this theory is equivalent to the homotopy algebraic $K$-theory introduced by Weibel.

Keywords

algebraic $K$-theory; descent; weight filtration

2010 Mathematics Subject Classification

18G60, 19D55

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