Séminaire de l’équipe AGA
Responsables : F. SCAVIA, M. TAMIOZZO
Mardi 9 septembre 2025
15:30 Haruzo Hida (UCLA) 
Résumé
Adjoint L-value and the Tate conjecture (séance exceptionnelle)
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13Lecture 1: We describe an explicit version of the Tate conjecture on
algebraic cycles for varieties over number fields and its background.
Then we sketch the strategy to prove the conjecture for a good amount
of quaternionic Shimura varieties.
Lecture 2: We give details of the proof of an explicit version of Tate
conjecture for quaternionic Shimura varieties. A key point is a
twisted adjoint L-value formula relative to each quaternion algebra
D_/F for a totally real field F
and its scalar extension B to E for a totally real quadratic
extension E/F. The theta base-change lift f_B of a Hilbert modular
form f on GL(2)/F to B^\times/E has non-vanishing period
integral over the Shimura subvariety Sh_D\subset Sh_B
given by the adjoint L-value at 1 twisted by the quadratic
character of E; so, Sh_D gives rise to a non-trivial explicit Tate
cycle in H^{2r}(Sh_B,C(r)) for r=\dim Sh_D=\dim Sh_B/2.
Vendredi 19 septembre 2025
10:30 João Lourenço (Université Sorbonne Paris Nord)
Titre bientôt disponible
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13
Vendredi 26 septembre 2025
10:30 Marc Levine (Universität Duisburg-Essen)
Titre bientôt disponible
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13
