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arXiv · 2212.06886

On the p-adic uniformization of quaternionic Shimura curves

Jean-Francois Boutot·Thomas Zink
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Abstract

Let D be a quaternion division algebra over a totally real number field F which splits exactly at one infinite place. We assume that there is a p-adic place where D doesn't split. Then the associated Shimura curve has a Cherednik unifomization by the p-adic upper half plane. We define an integral model of the Shimura curve an over the integers O of this p-adic place. We prove an uniformization theorem for the completion of the model over the formal spectrum Spf O.

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Jean-Francois Boutot, Thomas Zink. 2022-12-13. On the p-adic uniformization of quaternionic Shimura curves. https://arxiv.org/abs/2212.06886

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