Description:

Title: Chromatic homotopy theory in $H\mathbb{F}_{p}$ based Synthetic Spectra.

Abstract: Adams spectral sequence has been the most important computational tool in the stable homotopy theory whereas chromatic homotopy theory has allowed us to detect large scale patterns in the homotopy groups. It’s only natural to wish for a tool that will allow us to do both these procedures simultaneously. In this talk, I will show that by doing chromatic homotopy theory in ($H\mathbb{F}_{p}$ based) synthetic spectra, a gadget interpolating between topology and algebra which can also be thought of as a categorification of Adams spectral sequences, we can achieve that! This will naturally lead us to the study of tensor ideals of compact objects of synthetic spectra. I will end by stating and proving a version of Periodicity Theorem in this setting.