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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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Overconvergence and classicality: the case of curves

Payman L. Kassaei1

1Department of Mathematics, King's College London, Strand, London, WC2R 2LS, UK. e-mail:

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2009, Issue 631, Pages 109–139, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2009.043, March 2009

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Given our set-up of a system of abstract curves and maps between them satisfying certain assumptions, we prove a classicality criterion for overconvergent sections of line bundles over these curves. As a result we prove such criteria for overconvergent modular forms over various Shimura curves. In particular, we provide a classicality criterion for overconvergent modular forms studied in [Kassaei, Compos. Math. 140: 359–395, 2004] and their higher-level generalizations.

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Eyal Z. Goren and Payman L Kassaei
Comptes Rendus Mathematique, 2009, Volume 347, Number 17-18, Page 985

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