The rationality of Stark-Heegner cycles attached to Bianchi modular forms -- The base-change scenario

TL;DR

This paper investigates Stark-Heegner cycles linked to Bianchi modular forms over imaginary quadratic fields, confirming conjectures in the base-change case where the forms originate from classical elliptic cuspforms.

Contribution

It proves that Stark-Heegner cycle conjectures hold for Bianchi forms that are base-changed from classical elliptic cuspforms.

Findings

Conjectures verified for base-change Bianchi forms.

Establishes the relation between local cohomology classes and global Selmer groups.

Supports the broader conjectural framework of Stark-Heegner cycles.

Abstract

We study Stark-Heegner cycles attached to Bianchi modular forms, that is automorphic forms for GL(2) over an imaginary quadratic field F . The Stark-Heegner cycles are local cohomology classes in the p-adic Galois representation associated to the Bianchi eigenform. They are conjectured to be the restriction (at a prime p) of global cohomology classes in the (semistable) Bloch-Kato Selmer group defined over ring class fields of a relative quadratic extension K/F. In this paper, we show that these conjectures hold when the Bianchi eigenform is the base-change of a classical elliptic cuspform.