I will discuss a joint work with Ben-Moshe, Schlank, and Yanovski, proving the compatibility of T(n+1)-local algebraic K-theory with the formation of homotopy limits with respect to p-local π-finite group actions on T(n)-local categories. This is a generalization of the results of Thomason for height 0 and Clausen, Mathew, Naumann, and Noel for actions of discrete p-groups in arbitrary chromatic height. I will then discuss the compatibility of K-theory with the chromatic cyclotomic extensions, chromatic Fourier transform, and higher Kummer theory from previous works with Barthel, Schlank, and Yanovski, phenomena we refer to as “cyclotomic redshift”. Finally, I will explain how cyclotomic redshift gives hyperdescent for K-theory along the cyclotomic tower after K(n+1)-localization.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
