Tom Bachmann (MIT): Inverting spherical Bott elements

In joint work with Elden Elmanto and Paul Arne Oestvaer we extend etale descent results of Thomason, Levine and Elmanto-Levine-Spitzweck-Oestvaer. Specifically, over quite general base schemes, we construct self-maps of motivic Moore spectra whose telescopes satisfy etale hyperdescent. We also show that etale localization is smashing in our context, and consequently recover all the aforementioned etale descent results. In this talk I will give an overview of the proof of these results: I will explain our methods for constructing the self-maps, our use of the six functors formalism to reduce to the case of fields, and our use of the slice spectral sequence to reduce to Levine's etale descent theorem.