## Anticyclotomic main conjectures

### Summary

In this paper, we prove many cases of the anticyclotomic main conjecture for general CM fields with $p$-ordinary CM type.

### Mathematics Subject Classification

11R23, 11F27, 11F30, 11F33, 11F41, 11F60, 11F80, 11G15, 11G18, 11R34, 11R42

### Keywords/Phrases

Iwasawa theory, Main conjecture, CM field, anticyclotomic, Eisenstein series, CM abelian variety, Shimura series, Basis problem