Texed notes of my reading course last quarter advised by Yifeng Liu, with fellow participants Grisha Kondyrev and Jora Belousov. Our goal this reading course was understand some of Scholze’s recent work with perfectoid space techniques, in particular the proof of the monodromy weight conjecture.

Attached are only the notes I kept of my lectures, sometimes just outlines of what to talk about. I have had a few requests for these notes, and they are incomplete but I think they might still be helpful for others starting out in p-adic geometry.

During the reading course, I got the increasing feeling that we were just studying $G_Q$ as fast as our little legs could take us — our little legs being our knowledge of varieties (over various non-archimedian fields like $Q_p$ and $F_p((t))$. So, I finished with a talk on the Grothendieck-Teichmüller group — another approach to $G_Q$.