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.