Overconvergence and classicality: the case of curves

Details Overconvergence and classicality: the case of curves Overconvergence and classicality: the case of curves

2007-08-07

arxiv.org/abs/0708.0962v4

Mathematics

Number Theory

Scientific paper

Given our set-up of a system of 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: P-adic modular forms over Shimura curves over totally real fields, Compositio Math. 140 (2004), no 2, 359-395] and their higher-level generalizations.

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