Seminar on Torsion in the cohomology of locally symmetric varieties
The goal of this semester’s seminar is to learn about Scholze’s perfectoid spaces and in particular the applications of this theory to constructing Galois representations.
Date & place: Thu, 14-16, N-U-3.05
Program: pdf
Talks
| Title | Speaker | Date | |
|---|---|---|---|
| 1 | Overview and motivation | Ulrich Görtz | 10.4. |
| 2 | Adic spaces | Federico Binda | 17.4. |
| 3 | Almost ring theory | Lorenzo Mantovani | 24.4. |
| 4 | Perfectoid spaces | Rodolfo Venerucci | 8.5. |
| 5 | The canonical subgroup | Haifeng Wu | 22.5. |
| 6 | Canonical Frobenius lifts | Haifeng Wu | 5.6. |
| 7 | Tate’s normalized traces and the anti-canonical tower | Alexandre Pyvovarov | 12.6. |
| 8 | The Hodge-Tate spectral sequence | Jan Kohlhaase | 26.6. |
| 9 | The modular curve at infinite level and the HT period map | Giuseppe Ancona | 3.7. |
| 10 | Completed cohomology; comparison theorems | Shu Sasaki | 10.7. |
| 11 | Application: Galois representations | Vytas Paskunas | 17.7. |
Bibliography
O. Gabber, L. Ramero, Almost ring theory
R. Huber, Etale cohomology of rigid analytic varieties and adic spaces
P. Scholze, Perfectoid spaces, Publ. math. de l’IHÉS 116 (2012), no. 1, 245-313.
P. Scholze, Perfectoid spaces: a survey, Current Developments in Mathematics 2012, 193-227.
P. Scholze, Torsion in the cohomology of locally symmetric varieties
P. Scholze, $p$-adic Hodge theory for rigid-analytic varieties, Forum of Mathematics, Pi, 1, e1, 2013.
P. Scholze, J. Weinstein, Moduli of $p$-divisible groups, to appear in Cambridge Journal of Mathematics.
T. Wedhorn, Adic spaces
J. Weinstein, The geometry of Lubin-Tate spaces, Lecture notes
Videos
MSRI Hot topics workshop on perfectoid spaces, Feb. 2014.
Scholze on his Torsion paper at IHES, Oct. 2013
Weinstein, Modular Curves at infinite level, Notes and videos from Arizona Winter School 2013