English

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".

Keywords

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}
}
R2 v1 2026-06-22T11:13:03.458Z