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 "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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Submitted on : Saturday, October 17, 2015 - 10:57:14 AM
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Benjamin Schraen, Christophe Breuil, Eugen Hellmann. Smoothness and Classicality on eigenvarieties. Inventiones Mathematicae, Springer Verlag, 2017, 209 (1), pp.197--274. 〈https://doi.org/10.1007/s00222-016-0708-y〉. 〈10.1007/s00222-016-0708-y〉. 〈hal-01216803〉

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