On the Main Conjecture for CM Fields


The aim of this work is to prove a divisibility relation toward the main conjecture for CM fields. Our main tool is the study of congruences between an Eisenstein series and cusp forms on the unitary group GU(2,1). We introduce an Eisenstein ideal in the nearly-ordinary universal Hecke algebra for GU(2,1) and show that it divides the characteristic ideal of the CM Iwasawa module.