Smoothness and Classicality on eigenvarieties
Number Theory
2023-04-25 v1 Algebraic Geometry
Representation Theory
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 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".
Cite
@article{arxiv.1510.01222,
title = {Smoothness and Classicality on eigenvarieties},
author = {Christophe Breuil and Eugen Hellmann and Benjamin Schraen},
journal= {arXiv preprint arXiv:1510.01222},
year = {2023}
}