## V5A2 Selected Topics in Algebra: The Fargues-Fontaine curve - Wintersemester 2019/20

Contact:

Dr. Johannes Anschütz

Endenicher Allee 60 · Zimmer 4.027

**Tel.:** 0228-73-62216

** E-mail: ja **(ergänze @math.uni-bonn.de)

## 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".

## Prerequisites

Knowledge of valuations, p-adic fields and basic scheme theory.

## Lecture notes

Typed lecture notes are now available.

## Literature

- 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.

## Exercise sessions

There will be no exercise session accompanying the lecture.

## Exams

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.

*Last modified: April 2020, Johannes Anschütz*

## News

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