Lecture: p-adic geometry

The goal of this lecture is to cover the Berkeley lectures of Scholze-Weinstein and some more recent material.  

Lectures and exercises

First half of the lecture will be given by me and the second half by Torsten Wedhorn. 

There will be two lectures per week with exercises. The exercise session is covered by Thibaud van den Hove.

• Week 1: Valuations, Topological rings and non-archimedean fields (Exercise sheet 1) .

• Week 2: No lectures.

• Week 3: Huber rings and valuation spectra (Exercise sheet 2).

• Week 4: Examples and adic spaces (Exercise sheet 3).

• Week 5: Witt vectors, integral perfectoid rings and tilting (Exercise sheet 4 ).

• Week 6: Tilting equivalence and almost purity for perfectoid fields (Exercise sheet 5).

• Week 7: Perfectoid spaces, almost purity and totally disconnected spaces (Exercise sheet 6).

• Week 8: The pro-étale topology and diamonds (Exercise sheet 7)

Additional material: 

• Lecture notes of Johannes Anschütz on Lubin Tate spaces: Chapter 4

• Lecture notes of Georg Tamme

• Notes of Torsten Wedhorn

• Notes of Sophie Morel

• Notes of Katharina Hübner

• Lecture notes of Peter Scholze on Étale cohomology of diamonds

Schedule and streaming

The lectures will take place in person in Darmstadt in S2|15 401. The lecture will also be streamed and recorded via Zoom (link to the recordings). For access to the recordings please write a mail to me. 

• The lecture is scheduled at Mondays 9:50-11:30 and Wednesdays 11:40-13:20 starting from the week of the 14th October.

• The exercise session will take place Mondays 13:30-15:10 in person at S2|15 101 starting at the 28th of October. 

  • On the 11th and 25th of November there will be no exercises. Instead they will on the 7th and 21st of November (Thursday of the week before) from 9:50-11:30 at S2|15 315.