Smoothness and classicality on Eigenvarieties

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 weight and that its Galois representation is crystalline at places dividing p, then f is conjectured to be a classical automorphic form. We prove new cases of this conjecture in arbitrary dimension by making crucial use of the patched eigenvariety.