Abstract
We prove a gluing lemma for sections of line bundles on a rigid analytic variety. We apply the lemma in conjunction with a result of Buzzard [Bu, Theorem 5.2] to give a proof of (a generalization of) Coleman's theorem, which states that overconvergent modular forms of small slope are classical. The proof is geometric in nature and is suitable for generalization to other Shimura varieties
Citation
Payman L Kassaei. "A gluing lemma and overconvergent modular forms." Duke Math. J. 132 (3) 509 - 529, 15 April 2006. https://doi.org/10.1215/S0012-7094-06-13234-9
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