Iwasawa theory of Heegner points on abelian varieties of GL_2 type

TL;DR

This paper generalizes a key divisibility result from Iwasawa theory of Heegner points on elliptic curves to abelian varieties of GL2-type with real multiplication, broadening the scope of the main conjecture.

Contribution

It extends the divisibility result of Perrin-Riou's Iwasawa main conjecture from elliptic curves to abelian varieties of GL2-type over totally real fields.

Findings

Generalization of Iwasawa main conjecture divisibility to GL2-type abelian varieties

Application to abelian varieties associated with Hilbert modular forms

Broader understanding of Heegner points in Iwasawa theory

Abstract

In an earlier paper the author proved one divisibility of Perrin- Riou's Iwasawa main conjecture for Heegner points on elliptic curves. In the present paper, that result is generalized to abelian varieties of GL2-type (i.e. abelian varieties with real multiplication defined over totally real fields) under the hypothesis that the abelian variety is associated to a Hilbert modular form via a construction of Zhang.