V5A2 Selected Topics in Algebra: The Fargues-Fontaine curve - Wintersemester 2019/20
Time and Place
Wednesday, 14-16h, kleiner Hörsaal
First Lecture: Wednesday 16.10.2019.
Content of the course
We will introduce the fundamental curve of p-adic Hodge theory which was discovered by Fargues and Fontaine. It offers a geometric perspective on p-adic Hodge theory and is at the core of Fargues' program to geometrize the local Langlands correspondence. We will focus on the schematic version of the Fargues-Fontaine curve and prove some of its basic properties, e.g., that it is a Dedekind scheme. Using the classification of vector bundles on it we will derive the classical theorem that "weakly admissible" implies "admissible".
Knowledge of valuations, p-adic fields and basic scheme theory.
Lecture notesTyped lecture notes are now available.
- L. Fargues, J.-M. Fontaine: Courbes et fibrés vectoriels en théorie de Hodge p-adique. Asterisque 406, 2018
- L. Fargues and J.-M. Fontaine, Vector bundles on curves and p-adic Hodge theory. Automorphic forms and Galois representations. Vol. 2, 17–104, Cambridge, 2014.
- B. Bhatt, P. Scholze: Prisms and prismatic cohomology.
There will be no exercise session accompanying the lecture.
The oral exams scheduled for the 25.3.2020 are cancelled and will be postponed. The registered students will be contacted by me when more informations are available.