Perfectoid spaces (Math 679)

Time and location: 1:00pm - 2:30pm in 3096 East Hall, every Monday and Wednesday

Office hours: 2:30pm - 4:00pm, every Monday and Wednesday

A syllabus can be found here.

A preliminary version of the lecture notes written to accompany this class can be found here; these notes are very preliminary, missing attributions, not proofread, and subject to change without notice.

Live-TeXed notes for the class by Matt Stevenson can be found here.

We have an accompanying seminar on adic spaces, and the live-TeXed notes for the seminar by Matt Stevenson can be found here. See also Rankeya Datta's notes on Huber rings, and Takumi Murayama's notes on continuous valuations.


  • Scholze's thesis
  • Scholze's survey articles I and II
  • Notes from the Stanford seminar
  • Notes from MSRI's ``Hot topics'' workshop
  • Fontaine's Bourbaki talk notes
  • Gabber and Ramero's book on Almost ring theory
  • Huber's Continuous valuations and A generalization of formal schemes and rigid analytic varieties
  • Huber's book Etale cohomology of rigid analytic varieties and adic spaces (available through UM)
  • Wedhorn's notes on adic spaces