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arXiv · 1510.01222

Smoothness and Classicality on eigenvarieties

Christophe Breuil·Eugen Hellmann·Benjamin Schraen
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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".

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Christophe Breuil, Eugen Hellmann, Benjamin Schraen. 2015-10-05. Smoothness and Classicality on eigenvarieties. https://doi.org/10.1007/s00222-016-0708-y

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