Iwasawa theory of Heegner points on abelian varieties of GL2 type

Abstract

In an earlier paper [10], Howard proved one divisibility of Perrin-Riou's Iwasawa main conjecture for Heegner points on elliptic curves. In this 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.