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 structure of Bun_G for a general reductive G.

The seminar meets on Fridays 2:30pm--4:30pm at Kirwan Hall 3206 (UMD).


Schedule

Spring
1 February 6 Xintong Zhao Weakly admissible implies admissible
2 February 13 Xintong Zhao Weakly admissible implies admissible, II
3 February 20 Thomas Haines Projectivized Banach--Colmez spaces
4 March 2 Bogdan Zavyalov Upper semi-continuity of slopes
5 March 13 Thomas Haines Isocrystals with G-structure
6 March 27 Bogdan Zavyalov Bun_G and its underlying topological space
7 April 3 Qihang Li Beauville--Laszlo uniformization
8 April 10 Thomas Haines Local constancy of kappa
9 April 17 Xintong Zhao The semi-stable locus of Bun_G
10 April 24 Dori Bejleri The non-semistable locus of Bun_G
11 May 1
12 May 8
13 May 15

Useful links:

Papers:

Geometrization of the local Langlands correspondence, L. Fargues and P. Scholze
Courbes et fibres vectoriels en theorie de Hodge p-adique, L. Fargues and J.-M. Fontaine
Isocrystals with additional structure, R. E. Kottwitz
Isocrystals with additional structure. II, R. E. Kottwitz
On the classification and specialization of -isocrystals with additional structure, M. Rapoport and M. Richartz

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