On Iwasawa theory of Elliptic Units and 2-Ideal Class Groups

We use Euler systems to prove that, given an imaginary quadratic field k in which 2 splits completely, a prime p of k above 2 and a number field K₀ abelian with odd degree over k, then, in the unique Z2-extension of K unramified outside of p and abelian over k, the characteristic ideal of the projective limit of the 2-class groups divides the characteristic ideal of the projective limit of units modulo elliptic units. Our method follows closely the ideas of Rubin in [15].