Euler systems for conjugate-symplectic motives

Abstract: Kolyvagin's original Euler system (1990), based on Heegner points, complemented the height formula of Gross and Zagier to prove a key case of the Birch and Swinnerton-Dyer conjecture. I will introduce some new Euler systems. They are of a species theorized by Jetchev--Nekovar--Skinner, and pertain to those representations of the Galois group of a CM field that are automorphic, carry a conjugate-symplectic form, and have the simplest Hodge--Tate type.

The construction is based on Kudla's special cycles on unitary Shimura varieties, under an assumption of modularity for their generating series. Together with a recent height formula by Li--Liu and the forthcoming theory of JNS, this reduces some cases of the Beilinson--Bloch--Kato conjecture to the injectivity of Abel--Jacobi maps.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Columbia Automorphic Forms and Arithmetic Seminar