Séminaires : Séminaire Groupes Réductifs et Formes Automorphes

Equipe(s) : fa, tn,
Responsables :Alexis Bouthier, Benoît Stroh
Email des responsables : alexis.bouthier@imj-prg.fr, benoit.stroh@imj-prg.fr
Salle :
Adresse :

Orateur(s) Dimitar Jetchev - École polytechnique fédérale de Lausanne,
Titre Euler systems from special cycles on unitary Shimura varieties and arithmetic applications
Horaire10:30 à 12:00
We construct a new Euler system from a collection of special $1$-cycles on certain Shimura $3$-folds associated to $\mathrmU(2,1) \times \mathrmU(1,1)$ and appearing in the context of the Gan-Gross-Prasad conjectures. We study and compare the action of the Hecke algebra and the Galois group on these cycles via distribution relations and congruence relations obtain adelically using Bruhat-Tits theory for the corresponding buildings. If time permits, we explain some potential arithmetic applications in the context of Selmer groups and the Bloch-Kato conjectures for Galois representations associated to automorphic forms on unitary groups.