Duke Mathematical Journal

A gluing lemma and overconvergent modular forms

Payman L Kassaei

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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

Article information

Source
Duke Math. J. Volume 132, Number 3 (2006), 509-529.

Dates
First available: 1 April 2006

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1143935998

Digital Object Identifier
doi:10.1215/S0012-7094-06-13234-9

Mathematical Reviews number (MathSciNet)
MR2219265

Zentralblatt MATH identifier
05039111

Subjects
Primary: 11F33: Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50]
Secondary: 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35] 14G22: Rigid analytic geometry

Citation

Kassaei, Payman L. A gluing lemma and overconvergent modular forms. Duke Mathematical Journal 132 (2006), no. 3, 509--529. doi:10.1215/S0012-7094-06-13234-9. http://projecteuclid.org/euclid.dmj/1143935998.


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