This is the video of the lecture by Ben Antieau entitled "Cyclotomic Spectra and Dieudenné Modules 2". The talk was given on June 22, 2018 at the TU Berlin as part of the Homotopy Theory Summer Berlin.
The first part of the lecture series by Thomas Nikolaus can be watched here: vimeo.com/291281678
We will explain how to apply our joint work with Thomas Nikolaus on the cyclotomic t-structure to the topological Hochschild homology of schemes. In particular, we will describe the cyclotomic homotopy objects of smooth projective schemes over perfect fields of positive characteristic. This motivates the search for a connection between the classical notion of F-isocrystals and cyclotomic spectra. I will explain that there is a close, productive relationship between these two notions, which in fact allows us to classify isogeny classes of dualizable cyclotomic spectra over the topological Hochschild homology of algebraically closed fields of characteristic p.