Anticyclotomic Euler Systems for CM fields

Let $K\mathrm{/}F$ be a CM extension satisfying the ordinary assumption for an odd prime $p$ and let $\psi$ be a finite order anticyclotomic Hecke character of $K$. When $K$ has a place above $p$ of degree one, we apply Urban’s method and the results from our previous work to construct an anticyclotomic Euler system for $\psi$ under minor assumptions and prove one side o the divisibility of the anticyclotomic Iwasawa main conjecture for $\psi$ when $p$ is inverted.