---
abstract: 'Let $p$ be a prime number and $f$ an overconvergent $p$-adic automorphic form on a definite unitary group which is split at $p$. Assume that $f$ is of “classical weight” and that its Galois representation is crystalline at $p$, then $f$ is conjectured to be a classical automorphic form. We prove new cases of this conjecture in arbitrary dimensions by making crucial use of the patched eigenvariety constructed in [@BHS].'
address:
- |
    Christophe Breuil\
    C.N.R.S.\
    Laboratoire de Mathématiques d’Orsay\
    Université Paris-Sud\
    Université Paris-Saclay\
    F-91405 Orsay\
    France\
    Christophe.Breuil@math.u-psud.fr
- |
    Eugen Hellmann\
    Mathematisches Institut\
    Universität Bonn\
    Endenicher Allee 60\
    D-53115 Bonn\
    Germany\
    hellmann@math.uni-bonn.de
- |
    Benjamin Schraen\
    C.N.R.S.\
    Laboratoire de Mathématiques\
    Université de Versailles St. Quentin\
    45 Av. des États-Unis\
    F-78035 Versailles\
    France\
    benjamin.schraen@uvsq.fr
author:
- 'Christophe Breuil, Eugen Hellmann and Benjamin Schraen'
title: Smoothness and classicality on Eigenvarieties
---

Introduction
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Let $p$ be a prime number. In this paper we are concerned with classicality of $p$-adic automorphic forms on some unitary groups, i.e. we are looking for criteria that decide whether a given $p$-adic automorphic form is classical or not. More precisely we work with $p$-adic forms of finite slope, that is, in the context of 