I will discuss the problem of constructing a natural rational structure on periodic cyclic homology of dg-algebras and dg-categories. The promising candidate is A. Blanc’s topological K-theory. I will show that it, indeed, provides a rational structure in a number of cases and I will discuss its structural properties and possible applications.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/10868