Online Talk

Bokstedt periodicity displays the intricate nature of algebras over the sphere spectrum and is the cornerstone for all calculations of algebraic K-theory through trace methods. Shifting to a motivic context has proven to be a good way of shedding light on phenomena in stable homotopy theory that otherwise appear somewhat mysterious. Trying to uncover the nature of Bokstedt periodicity and its relation to chromatic homotopy theory we calculate motivic Hochschild homology in a variety of contexts and point at a specific case where the motivic calculation displays a shadow of higher chromatic phenomena beyond what the topological counterparts do.

Stable homotopy theory aside, knowing motivic Hochschild homology is strangely unexplored from the point of view of  understanding of motivic ring spectra more generally.  While much of what we do work more generally I will focus on the case where the base ring is an algebraically closed field, since information of the base scheme generally will complicate the expressions.