2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67161The cyclotomic trace of Bökstedt-Hsiang-Madsen, the subject of Bökstedt'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.Geometric Topology19D45, 19D50, 19D55, 11S70, 14F30, 55P91text