Algebraic $K$-theory and cubical descent

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, $KD(X)$, 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.