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.

  • 16.10.2019
  • 23.10.2019 (the lecture was given by Ben Heuer)
  • 30.10.2019
  • 06.11.2019
  • 13.11.2019
  • 20.11.2019
  • 27.11.2019
  • Because of the Dies Academicus there will be no lecture on 04.12.2019.
  • The lecture on 11.12.2019 will take place in SR 0.011!
  • 11.12.2019
  • 18.12.2019
  • 8.1.2020
  • 15.1.2020 (the lecture was given by Ben Heuer)
  • 22.1.2020
  • 29.1.2020

    • 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