On the p-adic uniformization of quaternionic Shimura curves

2022/12/13 by Boutot, Jean-Francois, Zink, Thomas
#14G20 #14H05 #Algebraic Geometry (math.AG) #FOS: Mathematics #G.m #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2212.06886

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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