Some remarks on topological 𝐾-theory of dg categories

Abstract

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