Darmon points on elliptic curves over number fields of arbitrary signature

TL;DR

This paper introduces new methods for constructing Darmon points on elliptic curves over various number fields, providing conjectures and numerical evidence for their global nature.

Contribution

It presents novel constructions of Darmon points over arbitrary signature fields, expanding the scope of previous work.

Findings

Numerical evidence supports the conjecture that these points are global.

New constructions apply to elliptic curves over diverse number fields.

The paper proposes conjectures on the global properties of these points.

Abstract

We present new constructions of complex and p-adic Darmon points on elliptic curves over base fields of arbitrary signature. We conjecture that these points are global and present numerical evidence to support our conjecture.