Smoothness and classicality on Eigenvarieties

• 成果类型: Article
• 署名作者: Breuil, Christophe; Hellmann, Eugen; Schraen, Benjamin
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; University of Munster; Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0708-y
• 发表日期: 2017
• 页码: 197-274
• 关键词: representations; distributions; families; forms

摘要

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 Breuil et al. (Math. Ann. 2016).