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-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 étale descent of topological K-theory of dg categories.

Final version; to appear in Proceedings of the AMS

References in corpus (2)

• Higher Topos Theory
• A1-homotopy theory of noncommutative motives

Cited by in corpus (2)

• Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds
• The homology of moduli stacks of complexes