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On the p-adic geometry of traces of singular moduli

Bas Edixhoven
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Abstract

The aim of this article is to show that p-adic geometry of modular curves is useful in the study of p-adic properties of traces of singular moduli. In order to do so, we partly answer a question by Ono. As our goal is just to illustrate how p-adic geometry can be used in this context, we focus on a relatively simple case, in the hope that others will try to obtain the strongest and most general results. For example, for p=2, a result stronger than Thm.1 is proved in [Boylan], and a result on some modular curves of genus zero can be found in [Osburn] . It should be easy to apply our method, because of its local nature, to modular curves of arbitrary level, as well as to Shimura curves.

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Bas Edixhoven. 2005-02-10. On the p-adic geometry of traces of singular moduli. https://doi.org/10.1142/s1793042105000327

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