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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Relèvement de formes modulaires de Siegel


Author: Benoît Stroh
Journal: Proc. Amer. Math. Soc. 138 (2010), 3089-3094
MSC (2010): Primary 11F33, 11G18, 11F46
Published electronically: May 11, 2010
MathSciNet review: 2653933
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Abstract: (Lifting Siegel modular forms). In this paper, we give explicit conditions under which cuspidal Siegel modular forms of genus $ 2$ or $ 3$ with coefficients in a finite field lift to cuspidal modular forms with coefficients in a ring of characteristic 0. This result extends a classical theorem proved by Katz for genus $ 1$ modular forms. We use ampleness results due to Shepherd-Barron, Hulek and Sankaran, and vanishing theorems due to Deligne, Illusie, Raynaud, Esnault and Viehweg.


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Additional Information

Benoît Stroh
Affiliation: Laboratoire Analyse, Géométrie et Applications, Institut Galilée, Université Paris 13, 93430 Villetaneuse, France
Email: benoit.stroh@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10378-5
PII: S 0002-9939(10)10378-5
Keywords: Siegel modular forms, toro\"\i dal compactifications, Kodaira vanishing theorem
Received by editor(s): January 13, 2009
Received by editor(s) in revised form: November 19, 2009
Published electronically: May 11, 2010
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.