2004/05/12 by Payman L Kassaei, Kassaei, Payman L · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.math/0405209
openalex publication_date 2004/05/12 · arxiv created 2006/01/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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's, 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 PEL Shimura varieties.