Miin-Lung Hsieh (McMaster)

On the main conjectures for CM fields.

The anticyclotomic main conjecture for CM fields is proved by Hida in many cases by studying the congruence ideal of CM forms on GL_2 over totally real fields. In this talk we will explain a proof of a divisibility relation toward both anticyclotomic and cyclotomic main conjectures for CM fields. The proof is based on the study on the congruences between Eisenstein series and cusp forms on the unitary group of degree three.