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arXiv · 0812.3231

Relevement de formes modulaires de Siegel

Benoit Stroh
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Abstract

Dans cette note, nous montrons que certaines formes modulaires de Siegel de caractéristique p et de genre 2 ou 3 se relèvent en caractéristique 0. Ce résultat généralise un théorème classique obtenu par Katz pour les formes de genre 1. Nous utilisons des résultats de Shepherd-Barron et de Hulek et Sankaran, ainsi que des théorèmes d'annulation de la cohomologie cohérente dûs à Deligne, Illusie et Raynaud et à Esnault et Viehweg. ----- In this note, we show that cuspidal Siegel modular forms of characteristic p and genus 2 or 3 can be lifted to 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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Benoit Stroh. 2010-03-31. Relevement de formes modulaires de Siegel. https://arxiv.org/abs/0812.3231

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