Séminaire de l’équipe AGA
Responsables : F. SCAVIA, M. TAMIOZZO
Vendredi 10 octobre 2025
10:30 Ananyo Kazi (UniDistance Suisse) 
Résumé
On p-adic L-functions and regulator formulas
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13The past decade has seen remarkable progress in the proof of the Bloch-Kato conjecture in analytic rank 0 for cohomological automorphic motives, whose critical L-values can be interpreted as period integrals over spherical pairs. A standard technique, developed by numerous people, uses p-adic interpolation – of Euler system classes, and of critical L-values of Dirichlet character twists of the motive – by linking them via an "explicit reciprocity law". A crucial ingredient in this technique is a syntomic regulator formula relating the Bloch-Kato logarithm of crystalline extension classes to p-adic L-values outside the range of classical interpolation. In this talk I will discuss ongoing work with Ting-Han Huang and Luca Marannino, on a new approach towards proving such regulator formulas. I'll focus on the example of the Asai motive of a quadratic Hilbert modular form, assuming p splits in the totally real field. This extends work of Grossi-Loeffler-Zerbes to the non-ordinary setting.
Vendredi 17 octobre 2025
10:30 Jörg Wildeshaus (Université Sorbonne Paris Nord) Résumé
Cohomologie à support compact et cohomologie bord des groupes arithmétiques
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13On exposera la définition et les propriétés des notions du titre. L'approche est pour l'essentiel basée sur l'article "Corners and Arithmetic Groups" de Borel-Serre. L'application principale concerne la dégénération des systèmes locaux dans la compactification de Baily-Borel des variétés de Shimura.
Vendredi 24 octobre 2025
10:30 Juan Esteban Rodriguez Camargo (Max Planck Institute for Mathematics (Bonn)) Résumé
De Rham stacks of Fargues-Fontaine curves
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13Using the theory of Analytic Geometry, we define the category of "Gelfand Stacks" that in particular generalises the category of Berkovich spaces (over Q_p). Within this category, we define analytic de Rham stacks of arc-stacks establishing some foundational properties. As an application, we study the analytic de Rham stacks of Fargues-Fontaine curves that ought to geometrize rigid and Hyodo-Kato cohomologies. Specialising to the case of the Fargues-Fontaine curve of C_p we give a new proof of the local p-adic monodromy theorem. Joint work with Anschütz, Bosco, Le Bras and Scholze.
