On the algebraicity of polyquadratic plectic points

TL;DR

This paper proves the algebraicity of plectic points linked to polyquadratic CM extensions and connects their non-vanishing to the ranks of elliptic curves, providing evidence of their arithmetic importance.

Contribution

It establishes the algebraicity of plectic points for polyquadratic CM extensions and relates their non-vanishing to elliptic curve ranks, advancing understanding of their arithmetic significance.

Findings

Proves algebraicity of plectic points for polyquadratic CM extensions

Links non-vanishing of plectic points to elliptic curve ranks

Provides evidence of the arithmetic significance of plectic Stark-Heegner points

Abstract

We establish direct evidence of the arithmetic significance of plectic Stark-Heegner points for elliptic curves of arbitrarily large rank. The main contribution is a proof of the algebraicity of plectic points associated to polyquadratic CM extensions of totally real number fields. Moreover, we relate the non-vanishing of plectic points to analytic and algebraic ranks of elliptic curves.