The Iwasawa-theoretic Gross-Zagier theorem

TL;DR

This paper proves a conjecture linking Heegner points in number field towers to a 2-variable p-adic L-function, extending previous p-adic Gross-Zagier results within Iwasawa theory.

Contribution

It establishes the Iwasawa-theoretic Gross-Zagier conjecture under certain conditions, advancing the understanding of the relationship between Heegner points and p-adic L-functions.

Findings

Proved the Iwasawa-theoretic Gross-Zagier conjecture under restrictive hypotheses.

Extended Perrin-Riou's p-adic Gross-Zagier theorem to a more general setting.

Connected Heegner points in towers of number fields to 2-variable p-adic L-functions.

Abstract

We prove Mazur and Rubin's Iwasawa-theoretic Gross-Zagier conjecture (under some restrictive hypotheses), which relates Heegner points in towers of number fields to the 2-variable p-adic L-function. The result generalizes Perrin-Riou's p-adic Gross-Zagier theorem.