Relèvement de formes modulaires de Siegel

Stroh, Benoît

doi:10.1090/S0002-9939-10-10378-5

Relèvement de formes modulaires de Siegel
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Proc. Amer. Math. Soc. 138 (2010), 3089-3094 Request permission

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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