An automorphic approach to Darmon points

TL;DR

This paper introduces a unified automorphic framework for constructing Darmon points on modular abelian varieties over various number fields, incorporating both archimedean and non-archimedean methods.

Contribution

It provides a novel, unified automorphic approach to Darmon points applicable to arbitrary number fields and central characters, expanding previous constructions.

Findings

Constructs Darmon points using archimedean and non-archimedean techniques.

Emphasizes the automorphic nature of the construction.

Applicable to arbitrary number fields with possibly non-trivial central characters.

Abstract

We give archimedean and non-archimedean constructions of Darmon points on modular abelian varieties attached to automorphic forms over arbitrary number fields and possibly non-trivial central character. An effort is made to present a unifying point of view, emphasizing the automorphic nature of the construction.