Séminaire de l’équipe AGA
Responsables : F. SCAVIA, M. TAMIOZZO
Vendredi 17 janvier 2025
10:30 Carlos Rivera (Université Sorbonne Paris Nord) 
Résumé
Reciprocity and local to global principles on p-adic function fields
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13In 2021, Olivier Wittenberg introduced a new obstruction to the local to global principle for varieties over $p$-adic function fields, the reciprocity obstruction, analogue to the Brauer-Manin obstruction for number fields, but unlike previous versions of it, including all divisorial valuation of the $p$-adic function field. We show a refinement theorem for the obstruction over blow ups of integral models of the $p$-adic function field, compare the obstruction with previous ones, construct some examples, and show the obstruction is the only one for connected $0$-dimensional varieties. We also define a reciprocity obstruction to the field patching method of Harbarter, Hartmann and Krashen, and use the refinement theorem to show it agrees with Wittenberg's version when both apply. This reduces the computation of the reciprocity pairings over all closed points of all integral models to a finite one. Finally, we analyse the existence of patch points in the field patching method from an analytic point of view, providing a conjectural reason for their existence.
Vendredi 24 janvier 2025
10:30 Marco Sangiovanni Vincentelli (Columbia University)
Titre bientôt disponible
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13
Vendredi 31 janvier 2025
10:30 David Lilienfeldt (Leiden University)
Titre bientôt disponible
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13
