# Euler systems from special cycles on unitary Shimura varieties and arithmetic applications

 Joint IAS/Princeton University Number Theory Seminar Topic: Euler systems from special cycles on unitary Shimura varieties and arithmetic applications Speaker: Dimitar Jetchev Affiliation: École Polytechnique Fédérale de Lausanne Date: Thursday, October 9 Time/Room: 4:30pm - 5:30pm/Fine 214, Princeton University

We construct a new Euler system from a collection of special 1-cycles on certain Shimura 3-folds associated to $U(2,1) \times U(1,1)$ 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.