p-adic functoriality for inner forms of unitary groups in three variables

TL;DR

This paper establishes p-adic functoriality for inner forms of unitary groups in three variables by constructing morphisms between eigenvarieties, extending classical Langlands functoriality to the p-adic setting.

Contribution

It introduces a new method to realize p-adic functoriality for specific unitary groups via eigenvariety morphisms, advancing the understanding of p-adic Langlands correspondences.

Findings

Constructed morphisms between eigenvarieties for inner forms of unitary groups.

Extended classical Langlands functoriality to the p-adic context.

Provided evidence for the compatibility of p-adic and classical functoriality.

Abstract

We prove p-adic functoriality for inner forms of unitary groups in three variables by establishing the existence of morphisms between eigenvarieties that extend the classical Langlands functoriality.