×

Algebraic \(K\)-theory and cubical descent. (English) Zbl 1221.19002

Summary: 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, \(\mathcal{KD}(X)\), 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 \(K\)-theory introduced by Weibel.

MSC:

19D55 \(K\)-theory and homology; cyclic homology and cohomology
18G60 Other (co)homology theories (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI arXiv Link