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


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.


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


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

Further resources

Oberseminar Bonn

Oberseminar Bielefeld Paderborn

Notes from perfectoid reading group at U. Chicago