Algebraic K-theory and cubical descent

Details Algebraic K-theory and cubical descent Algebraic K-theory and cubical descent

2007-06-15

arxiv.org/abs/0706.2257v2

Mathematics

Algebraic Geometry

18 pages

Scientific paper

In this note we apply Guillen-Navarro descent theorem, \cite{GN02}, to define a descent variant of the algebraic $K$-theory of varieties over a field of characteristic zero, $\mathcal{KD}(X)$, which coincides with $\mathcal{K}(X)$ for smooth varieties. After a result of Haesemeyer, this new theory is equivalent to the homotopy algebraic $K$-theory introduced by Weibel. We also prove that there is a natural weight filtration on the groups $KH_\ast(X)$.

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