  We show existence of a natural rational structure on periodic cyclic
homology, conjectured by L. Katzarkov, M. Kontsevich, T. Pantev, for several
classes of dg-categories, including proper connective $\mathbb{C}$-dg-algebras
and dg-categories of local systems. The main ingredient is derived nilpotent
invariance of A. Blanc's semi-topological K-theory, which we establish along
the way.
