MATH 6370 p-adic Hodge Theory (Spring 2025)

Instructor: Daniel Gulotta, dgulotta@math.utah.edu
Location and time: MWF 9:40-10:30 in AEB 306
Credits: 3
Office hours: time TBA in JWB 106
Grading: If you are an undergraduate and need a grade for the course, let me know.

References

We will cover chapters 1-9 of [BC] and chapters 1-8 of [FO] (these two references cover roughly the same material), chapters 2-13 of [SW], and some additional topics, likely including [S], [BS], [BL].

Notes will be posted here after each class.

Main references

[BC] O. Brinon and B. Conrad, CMI summer school notes on p-adic Hodge theory
[BL] B. Bhatt and J. Lurie, Absolute prismatic cohomology
[BS] B. Bhatt and P. Scholze, Prisms and prismatic cohomology
[FO] J.-M. Fontaine and Y. Ouyang, Theory of p-adic Galois representations
[S] P. Scholze, p-adic Hodge theory for rigid analytic varieties
[SW] P. Scholze and J. Weinstein, Berkeley lectures on p-adic geometry

Other references

[M] J. Milne, Field theory and Galois theory

Here is a link to a course on p-adic Hodge theory that I taught in 2020.

If you are looking for exercises, there are some in [BC] and in these two references:

H. Diao, Period rings and period sheaves
Y. Mieda, Adic spaces and perfectoid spaces

Tentative Schedule

Date	Topic	References
1/6	Introduction
1/8	Infinite Galois theory	[M] 3, 7
1/10	Infinite Galois theory, examples of Galois representations	[M] 3, 7, [BC] 1, [FO] 2
1/13	Examples of Galois representations, p-adic fields	[BC] 1, [FO] 1.2, 2
1/15	φ-modules	[BC] 3, [FO] 3.2