Séminaire de l’équipe AGA
Responsables : F. SCAVIA, M. TAMIOZZO
Vendredi 21 novembre 2025
10:30 Arnaud Eteve (Max Planck Institute for Mathematics (Bonn)) 
Résumé
Local-global compatibility over fields
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13This is based on joint works with D. Gaitsgory, V. Lafforgue and A. Genestier and with C. Xue. Let $X$ be a smooth proper curve over a finite field, $G$ be a reductive group over $X$ and $v \in X$ be a closed point. The goal of this talk is to discuss two related structures :
- in the local situation, I will report on the construction of a spectral action on the category of sheaves on the stack of $G$-isocrystals (over the completion of the function field of $X$ at $v$). This construction provides a geometrization of the local Langlands correspondence. This can be considered, in particular, an algebraic counterpart to the construction of Fargues-Scholze and the two theory are conjecturally equivalent.
- in the global situation, the structure at play here is given by the construction of certain coherent sheaves on the stack of global Langlands parameters whose role is to organize the various cohomology groups of stacks of global $G$-shtukas and provides a conceptual explanation to V. Lafforgue's theory of excursion operators.
The precise relation between these objects gives a strong form of local-global compatibility.
Vendredi 28 novembre 2025
10:30 Jean-Louis Colliot-Thélène (Orsay)
Titre bientôt disponible
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13
Vendredi 5 décembre 2025
10:30 Luca Marannino (Jussieu)
Titre bientôt disponible
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13
Vendredi 12 décembre 2025
10:30 João Lourenço (USPN)
Titre bientôt disponible
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13
Vendredi 19 décembre 2025
10:30 Pierre Charollois (Jussieu)
Titre bientôt disponible
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13
