On Anticyclotomic Iwasawa Theory of Hecke Characters at Ordinary Primes

Abstract: In this article we study the Iwasawa theory for Hecke characters associated with CM abelian varieties and Hilbert modular forms at ordinary primes. We formulate and prove a result concerning the anticyclotomic Iwasawa main conjecture for CM Hilbert modular forms. Additionally, we obtain a result towards the study of the Mordell-Weil ranks of the CM abelian varieties.