Ordinary representations and companion points for U(3) in the indecomposable case

TL;DR

This paper demonstrates that specific p-adic Banach representations linked to local ordinary Galois representations are present in the completed cohomology of a definite unitary group in three variables, confirming part of Breuil and Herzig's conjecture.

Contribution

It establishes the appearance of certain p-adic Banach representations in completed cohomology, advancing understanding of automorphic forms and Galois representations for U(3).

Findings

Confirmation of Breuil and Herzig's conjecture in the indecomposable case.

Identification of p-adic Banach representations in completed cohomology.

Use of eigenvarieties to analyze automorphic forms for U(3).

Abstract

We prove that certain p-adic Banach representations, associated to local ordinary Galois representations, constructed by Breuil and Herzig appears in the completed cohomology of a definite unitary group in three variables. This confirms part of their conjecture. Our main technique is making use of p-adic automorphic forms for definite unitary groups and the eigenvarieties which parameterize them.