Overconvergent cohomology and quaternionic Darmon points

TL;DR

This paper advances the construction and computation of quaternionic Darmon points using overconvergent cohomology, providing the first numerical evidence for their rationality conjectures.

Contribution

It develops new (co)homological tools and applies overconvergent cohomology techniques to efficiently compute and analyze quaternionic Darmon points.

Findings

Effective construction of quaternionic Darmon points

Efficient computational methods using overconvergent cohomology

Numerical evidence supporting rationality conjectures

Abstract

We develop the (co)homological tools that make effective the construction of the quaternionic Darmon points introduced by Matthew Greenberg. In addition, we use the overconvergent cohomology techniques of Pollack--Pollack to allow for the efficient calculation of such points. Finally, we provide the first numerical evidence supporting the conjectures on their rationality.