Fargues--Scholze Learning Seminar I: the Fargues--Fontaine curve, 2025

This is a learning seminar on the ``Geometrization of the local Langlands correspondence''. The goal is to understand the Fargues--Fontaine curve and prove the classification of vector bundles on it.

The seminar meets on Fridays 2:00pm--4:00pm at Kirwan Hall 3206 (UMD).


Schedule

Spring
1 September 19 Thomas Haines Introduction to the Fargues-Scholze geometrization theorem
2 September 26 Thomas Haines Introduction to the Fargues-Scholze geometrization theorem II
3 October 3 Bogdan Zavyalov Fargues--Fontaine Curve I. Analytic curve
4 October 10 Dori Bejleri Fargues--Fontaine curve II: algebraic FF curve
5 October 17 Dori Bejleri Fargues--Fontaine curve II: algebraic FF curve (continued)
6 October 24 Ziyi Huang Pro-etale topology, v-topology, and diamonds
7 October 31 Ziyi Huang More on diamonds, and degree 1 Cartier divisors on the Fargues-Fontaine curve
8 November 14 Anurag Kumar Lubin-Tate Theory and O(1)
9 November 21 Bogdan Zavyalov Local class field theory, d'apres Fargues
10 December 5, Bogdan Zavyalov Local class field theory, d'apres Fargues (continued)
11 December 12 Dori Bejleri Classification of vector bundles on the Fargues--Fontaine curve

Useful links:

Papers:

Geometrization of the local Langlands correspondence, L. Fargues and P. Scholze
Simple connexite des fibres d'une application d'Abel-Jacobi et corps de classe local, L. Fargues
Courbes et fibres vectoriels en theorie de Hodge p-adique, L. Fargues and J.-M. Fontaine

Notes:

Geometrization of the local Langlands correspondence (the course), Scholze's course on the subject (video lectures and handwritten notes)
Geometrization of the local Langlands correspondence (the course), Notes by Tony Feng
Geometrization of the Local Langlands Correspondence: an overview, Laurent Fargues
Eilenberg/Hausdorff lectures on the geometrization of the Local Langlands Correspondence, Laurent Fargues
Montreal lectures: Geometrization of the Local Langlands Program, Notes by Tony Feng
Arbeitsgemeinschaft: The Geometric Langlands, Oberwolfach report
The geometrization of local Langlands [after L. Fargues and P. Scholze], Ana Caraiani