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RELÈVEMENT DE FORMES MODULAIRES DE SIEGEL
Proceedings of the American Mathematical Society
Vol. 138, No. 9 (SEPTEMBER 2010), pp. 3089-3094
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/20764265
Page Count: 6
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(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.
Proceedings of the American Mathematical Society © 2010 American Mathematical Society