  Using techniques from motivic homotopy theory, we prove a conjecture of
Anthony Blanc about semi-topological K-theory of dg categories with finite
coefficients. Along the way, we show that the connective semi-topological
K-theories defined by Friedlander-Walker and by Blanc agree for
quasi-projective complex varieties and we study \'etale descent of topological
K-theory of dg categories.
