I am trying to undesrtand the analogy between the Euler systems over abelian extensions of the rationals and the Euler systems over abelian extensions of imaginary quadratic fields.
As Soogil Seo explains in his paper "Circular Distributions and Euler Systems" any Euler system over abelian extensions of the rationals can be obtained from cyclotomic units. However, I am struggling with understanding if the same statement is true about imaginary quadratic extensions i.e. if all Euler systems over abelian extensions of imaginary quadratic fields come from elliptic units (which are the analogous of cyclotomic units in the imaginary quadratic case).
I understand how elliptic units can be made into Euler systems and how they are used by Rubin in proving the main conjecture in the imaginary quadratic extension. But I find it difficult to understand how elliptic units can generate the module of Euler systems in abelian extensions the imaginary quadratic fields case. Any help would be appreciated.