Geometry of the Bianchi eigenvariety around non-cuspidal points and strong multiplicity-one results

TL;DR

This paper investigates the local geometric structure of the Bianchi eigenvariety near non-cuspidal points, introducing Bianchi Eisenstein eigensystems and establishing strong multiplicity-one results for Bianchi threefold cohomology.

Contribution

It introduces Bianchi Eisenstein eigensystems and proves strong multiplicity-one results, advancing understanding of the eigenvariety's local geometry around non-cuspidal points.

Findings

Analysis of local geometry around non-cuspidal points

Introduction of Bianchi Eisenstein eigensystems

Proof of strong multiplicity-one results

Abstract

Let $K$ be an imaginary quadratic field. In this article, we study the local geometry of the Bianchi eigenvariety around non-cuspidal classical points, in particular, ordinary non-cuspidal base change points. To perform this study we introduce Bianchi Eisenstein eigensystems and prove strong multiplicity-one results on the cohomology of the corresponding Bianchi threefolds. We believe these results are of independent interest.