Morningside Center of Mathematics

Chinese Academy of Sciences

**The Curve and p-adic Hodge theory**

**Speaker:** Prof. Laurent Fargues

The main theme of this course will be to understand and give a meaning to the notion of a p-adic Hodge structure. Starting with the work of Fontaine, who introduced many of the basic notions in the domain, it took many years to understand the exact definition of a p-adic Hodge structure. We now have the right definition: this involves the fundamental curve of p-adic Hodge theory and vector bundles on it. In the course I will explain the construction and basic properties of the curve. I will moreover explain the proof of the classification of vector bundles theorem on the curve. As an application I will explain the proof of weakly admissible implies admissible. In the meanwhile I will review many objects that show up in p-adic Hodge theory like p-divisible groups and their moduli spaces, Hodge-Tate and de Rham period morphisms, and filtered phi-modules.

**Place:** MCM 110

**Time:** 10:00-12:00, each Friday, during Nov. 1, 2019 - Jan. 10, 2020.

two exceptions:

(1) Nov. 29 changed to Nov. 26, 10:00-12:00

(2) Dec. 6 changed to Dec. 5, 15:00-17:00

**References:**

- "Courbes et fibrés vectoriels en théorie de Hodge p-adique" L. Fargues and J.-M. Fontaine, Asterisque 406
- Notes from a series of lectures at the Drinfeld seminar
- Notes from a course gave in Jussieu