Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Angelini-Knoll, Gabriel, Quigley, J. D.
Format: Preprint
Veröffentlicht: 2019
Schlagworte:
Online-Zugang:https://arxiv.org/abs/1908.09164
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Inhaltsangabe:
  • The family of Thom spectra $y(n)$ interpolates between the sphere spectrum and the mod two Eilenberg--MacLane spectrum. Computations of Mahowald, Ravenel, Shick, and the authors show that the associative ring spectrum $y(n)$ has type $n$. Using trace methods, we give evidence that algebraic K-theory preserves this chromatic complexity. Our approach sheds light on the chromatic complexity of topological negative cyclic homology and topological periodic cyclic homology, which approximate algebraic K-theory and are of independent interest. Our main contribution is a homological approach that can be applied in great generality, such as to associative ring spectra $R$ without additional structure whose coefficient rings are not completely understood.