  The cyclotomic trace of B\"okstedt-Hsiang-Madsen, the subject of B\"okstedt's
lecture at the congress in Kyoto, is a map of pro-abelian groups K_*(A) ->
TR_*^.(A;p) from Quillen's algebraic K-theory to a topological refinement of
Connes' cyclic homology. Over the last decade, our understanding of the target
and its relation to K-theory has been significantly advanced. This and possible
future development is the topic of my lecture.
