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, KD(X), which coincides with 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.
algebraic K-theory; descent; weight filtration
Pascual, P., Rubió, L. Algebraic K-theory and cubical descent. "Homology homotopy and applications", 2009, vol. 11, núm. 2, p. 5-25.