Plectic Stark-Heegner points

TL;DR

The paper introduces a conjectural method to construct global points on modular elliptic curves over any number field, extending existing theories and linking p-adic L-functions to the Mordell-Weil group via plectic Stark-Heegner points.

Contribution

It proposes a new conjectural framework for plectic Stark-Heegner points that generalizes previous constructions and connects p-adic L-functions to elliptic curve ranks.

Findings

Evidence from derivatives of p-adic L-functions supports the conjectures.

The construction extends classical Stark-Heegner points to a broader setting.

The approach aligns with plectic conjectures relating to Mordell-Weil groups.

Abstract

We propose a conjectural construction of global points on modular elliptic curves over arbitrary number fields, generalizing both the p-adic construction of Heegner points via Cerednik-Drinfeld uniformization and the definition of classical Stark-Heegner points. In alignment with Nekovar and Scholl's plectic conjectures, we expect the non-triviality of these plectic Stark-Heegner points to control the Mordell-Weil group of higher rank elliptic curves. We provide some indirect evidence for our conjectures by showing that higher order derivatives of anticyclotomic p-adic L-functions compute plectic invariants.