Anticyclotomic Euler Systems for CM fields

Let $K/F$ be a CM extension satisfying the ordinary assumption for an odd prime p and let $ψ$ 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 $ψ$ under minor assumptions and prove one side o the divisibility of the anticyclotomic Iwasawa main conjecture for $ψ$ when p is inverted.