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