$p$-adic Langlands functoriality for the definite unitary group

TL;DR

This paper extends the classical Langlands functoriality to the $p$-adic setting for definite unitary groups, using eigenvarieties and interpolation of known cases.

Contribution

It formalizes a $p$-adic Langlands functoriality framework for definite unitary groups, bridging classical and $p$-adic theories via eigenvarieties.

Findings

Establishes a formal notion of $p$-adic Langlands functoriality

Interpolates classical cases to $p$-adic setting

Provides new cases of $p$-adic functoriality

Abstract

We formalise a notion of $p$-adic Langlands functoriality for the definite unitary group. This extends the classical notion of Langlands functoriality to the setting of eigenvarieties. We apply some results of Chenevier to obtain some cases of $p$-adic Langlands functoriality by interpolating known cases of classical Langlands functoriality.