The $p$-adic variation of the Gross-Kohnen-Zagier theorem

TL;DR

This paper explores the relationship between p-adic families of Jacobi forms and Big Heegner points, framing it within a p-adic Kudla program and extending the Gross-Kohnen-Zagier theorem to a p-adic context.

Contribution

It introduces a novel connection between p-adic Jacobi forms and Big Heegner points, providing a new perspective on the p-adic Kudla program for GL(2).

Findings

Establishes a link between p-adic Jacobi forms and Big Heegner points.

Frames the results within a p-adic Kudla program.

Extends the Gross-Kohnen-Zagier theorem to a p-adic setting.

Abstract

We relate $p$-adic families of Jacobi forms to Big Heegner points constructed by B. Howard, in the spirit of the Gross-Kohnen-Zagier theorem. We view this as a GL(2) instance of a $p$-adic Kudla program.