Introduction to p-adic Hodge Theory

Course Description

In this course, we will give an introduction to p-adic Hodge theory and we will focus on the geometric aspect of this theory.

Possible topics includes:

1 p-divisible groups and abelian varieties, Hodge-Tate decomposition for p-divisible groups, deformations of p-divisible groups.

2 p-adic representations, Fontaine’s period rings.

3 p-adic comparison theorems.


The choice of material will be based on the interests and prerequisites of the participants.


Berger, Laurent, An introduction to the theory of p-adic representations, Geometric aspects of Dwork theory, I, Berlin: Walter de Gruyter GmbH & Co. KG,

Brinon, Olivier; Conrad, Brian, CMI Summer School notes on p-adic Hodge theory

J-M. Fontaine, Groupes p-divisibles sur les corps locaux, Société Mathématique de France, Astérisque, No. 47-48, 1977.

J-M. Fontaine, Sur certains types de représentations p-adiques du groupe de Galois d’un corps local ; construction d’un anneau de Barsotti–Tate, Annals of Math. (2) 115 (1982), no. 3, pp. 529–577.

J-M. Fontaine, "Arithmétique des représentations galoisiennes p-adiques" in Cohomologies p-adiques et applications arithmétiques (III), Astérisque 295 (2004), pp. 1–115.

A. Grothendieck, Groupes de Barsotti-Tate et cristaux de Dieudonné, Sém. Math. Sup. 45, Presses de l'Université de Montréal, 1974.

L. Illusie, Déformations de groupes de Barsotti-Tate, d'après A. Grothendieck, in Séminaire sur les pinceaux arithmétiques : la conjecture de Mordell, Lucien Szpiro, Astérisque 127, SMF, 1985, 151-198.

J. Tate, "p-divisible groups” in Proc. Conf. on Local Fields (Driebergen), Springer-Verlag, 1967, pp. 148–183.

Course Meeting Time and Location
Tuesday and Thursday
2:30 - 3:55 pm
122 Math Building (Building 15)

Course Instructor Contact Information and Office Hours
Dr. Daxin Xu
210-4 Math Building (Building 15)
Office Hour: By email appointments

Course Schedule and Textbook

Course Policies

Midterm and Final Exam

Daxin XU,
Oct 31, 2017, 4:08 PM
Daxin XU,
Oct 11, 2017, 7:14 PM
Daxin XU,
Oct 11, 2017, 7:29 PM