# Integral \(p\)-adic Hodge Theory

A summer reading seminar co-organized by Raymond Cheng and Shizhang LiThe aim of this seminar is to gain an understanding of the (relatively) recent work of Bhatt–Morrow–Scholze on integral \(p\)-adic Hodge theory.

## References

The primary reference, of course, is the paper of Bhatt–Morrow–Scholze listed below. Besides that, however, Bhatt and Morrow have each written additional articles that explain specific aspects of the main paper.

Bhargav Bhatt, Matthew Morrow, and Peter Scholze, Integral \(p\)-adic Hodge theory.

Bhargav Bhatt, Specializing varieties and their cohomology from characteristic \(0\) to characteristic \(p\).

Matthew Morrow, Notes on the \(\mathbf{A}_{\mathrm{inf}}\) cohomology of Integral \(p\)-adic Hodge theory.

## Schedule

We meet Thursdays in Mathematics Room 407 between 2:00PM and 3:30PM.

- 05/17
- Shizhang Li,
- Background.
- [§§1–4, Bhatt].
- 05/24
- Shizhang Li,
- Almost Purity and Primitive Comparison.
- 05/31
- Qixiao Ma,
- \(L\eta\).
- [§5, Bhatt], [§6, BMS].
- 06/07
- TBA,
- The complex \(\widetilde\Omega_{}\).
- [§6, Bhatt], [§8, BMS].
- 06/14
- Shizhang Li,
- Breuil–Kisin–Fargues modules.
- [§4, BMS].
- 06/21
- Shizhang Li,
- Rational \(p\)-adic Hodge theory.
- [§5, BMS].
- 06/28
- Zijian Yao,
- The complex \(A\Omega_{\mathfrak{X}}\).
- [§7, Bhatt], [§9, BMS].
- 07/05
- Qixiao Ma,
- Global results.
- [§8, Bhatt].
- 07/12
- Shizhang Li.
- Relative de Rham–Witt complex.
- [§10, BMS].
- 07/19
- Raymond Cheng.
- Comparison with de Rham–Witt complexes.
- [§11, BMS].
- 07/20
- Zijian Yao,
- Comparison with crystalline cohomology over \(A_\mathrm{crys}\).
- [§12, BMS].
- 07/26
- TBA,
- Proof of main theorems.
- [§14, BMS].