Time: 10:00-11:30, 12:30-14:00   9/22, 9/29, 10/13, 10/20, 10/27 (online)

Zoom ID：828 4332 7340
Password：653300

This short course is an introduction to the perfectoid space theory and its applications to p-adic Hodge theory following Scholze. 

We will discuss following topics:

(i) Perfectoid fields and algebras; almost mathematics;

(ii) Adic space and perfectoid space;

(iii) Pro-\'etale topology and comparison theorems. 

Prerequisites: 
(i) algebraic geometry: one should be familiar with chapters 1-3 of GTM52; it is helpful to have some knowledge on rigid-space e.g., to have read [1], but it is not an obligation.
(ii) algebraic number theory: one should be familiar with [2].
References:
[1] S. Bosch, Lectures on formal and rigid geometry. Vol. 2105. Springer, 2014.
[2] J.-P. Serre, Local fields. Translated from the French by Marvin Jay Greenberg. Graduate Texts in Mathematics, 67. Springer-Verlag, New York-Berlin, 1979. viii+241 pp.
[3] P. Scholze, Perfectoid spaces. Publications mathématiques de l'IHÉS, 116(1), 245-313. (2012).
[4] P. Scholze, p-adic Hodge theory for rigid-analytic varieties, Forum of Mathematics, Pi, 1, e1, (2013).