The seminar on Shimura varieties with infinite level structure at p will be held during the winter term 2013/14 in cooperation with the universities Bielefeld and Paderborn. As a preparation there will be a pre-seminar on perfectoid spaces.
It is the aim of the seminar to understand Scholzes perfectoid spaces and to acquire the required knowledge for the seminar on Shimura varieties with infinite level structure at p.
The seminar will take place on three different days:
- Saturday, 28th September, 2013, from 9am at room MI 02.08.20
- Sunday, 29th September, 2013, from 9 am at room MI 02.08.20
- Monday, 30th September, 2013, from 10 am at room MI 02.08.20
The topics of the first and second day are self-contained and may also be of interest to those who do not want to learn about perfectoid spaces. We give a outline of the topics:
1st day: Falting's almost mathematic, perfectoid algebras. As an application of the theory we show that the absolute Galois groups of Qp(p1/p∞) and Fp(t1/p∞) are isomorphic.
2nd day: An introduction to adic spaces.
3rd day: Perfectoid spaces.
The goal of this seminar is to understand Peter Scholze's paper "On torsion in the cohomology of locally symmetric varieties".
It will be held in cooperation with the Oberseminar Algebra und Geometrie of the universities Bielefeld and Paderborn. There will be three common sessions and all remaining talks will be given in Bielefeld/Paderborn and at the TUM separately.
Program: pdf (Warning: This is the program for Bielefeld/Paderborn; for the times and places of the talks for TUM-people see below)
1. Talk: 30th October 2013, 10:15-11:45, Stephan Neupert: A comparison theorem for the cohomology of adic spaces (Talk 7 in the program)
2. Talk: 8th November 2013, 14:15-15:45, Paul Hamacher: The Hodge-Tate-filtration (Talk 8 in the program)
3. Talk: 11th November 2013 (rescheduled to 27th November 2012, 10:05 - 11:35), Alex Ivanov: The relation to Fargue's Hodge-Tate-filtration for p-divisible groups (Talk 8 in the program)
4. Talk: 11th November 2013, 10:15-11:45, Bernhard Werner: The canonical subgroup (Talk 2 in the program)
5. Talk: 13th November 2013, 15:00-16:30 in Paderborn, Chuangxun Cheng (Uni Paderborn): Canonical Frobenius lifts - the good reduction case (Talk 3 in the program)
6. Talk: 13th November 2013, 16:45-18:15 in Paderborn, Lennart Gehrmann (Uni Paderborn): Canonical Frobenius lifts - extension to the boundary (Talk 4 in the program)
7. Talk: 16th December 2013, 12:30-14:00, Bernhard Werner: Tate’s normalised trace (Talk 5 in the program)
8. Talk: 16th December 2013, 14:15-15:45, Paul Hamacher: A tubular neighborhood of the anticanonical tower is perfectoid (Talk 6 in the program)
9. Talk: 8th January 2014, 14:45-16:15 in Bielefeld, Stephan Neupert: Hodge-Tate period map (Talk 9 in the program)
10. Talk: 8th January 2014, 16:30-18:00 in Bielefeld, Alex Ivanov: p-adic automorphic forms (Talk 10 in the program)
11. Talk: 22th January 2014, 15:00-16:30 in Paderborn, Hendrik Verhoek (Uni Bielefeld): Galois representations I (Talk 11 in the program)
12. Talk: 22th January 2014, 16:45-18:15 in Paderborn, Thomas Zink (Uni Bielefeld): Galois representations II (Talk 12 in the program)