Rational homotopy of the K(n)-local sphere

In Spring 2024, the babytop seminar was about the two (p-adic) towers and the paper “On the rationalization of the K(n)-local sphere” by Barthel, Schlank, Stapleton, and Weinstein. I gave the last talk of the semester, explaining how to finish the proof of Theorem B by computing the proétale cohomology of the Drinfeld symmetric space and the rigid analytic open unit disc. My talk covered Sections 6 and 3.9 of the paper.