On Anticyclotomic Iwasawa Theory of Hecke Characters at Ordinary Primes

TL;DR

This paper advances the understanding of anticyclotomic Iwasawa theory for Hecke characters linked to CM abelian varieties and Hilbert modular forms at ordinary primes, proving a main conjecture and exploring Mordell-Weil ranks.

Contribution

It formulates and proves a main conjecture in anticyclotomic Iwasawa theory for CM Hilbert modular forms and investigates Mordell-Weil ranks of CM abelian varieties.

Findings

Proved the anticyclotomic Iwasawa main conjecture for CM Hilbert modular forms.

Established results relating to Mordell-Weil ranks of CM abelian varieties.

Enhanced understanding of Iwasawa theory in the context 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.