Local points of twisted Mumford quotients and Shimura curves
This paper continues earlier work of the first two authors [Math. Ann. 270, 235--248 (1985; Zbl 0536.14018)] in studying the existence of local points on Shimura curves. In the archimedean case, this was done by \textit{G. Shimura} [Math. Ann. 215, 135--164 (1975; Zbl 0394.14007)]. While the earlier study of Jordan and Livné uses a direct analysis of the geometric properties of the curve, this paper addresses the problem via the theory of \(p\)-adic uniformisation due to the last author and to Rapoport-Zink. As a final application, the authors use their theory to construct some Shimura curves over real quadratic fields with odd narrow class number (and under certain additional hypotheses) which are even in the sense of \textit{B. Poonen} and \textit{M. Stoll} [Ann. Math. (2) 150, 1109--1149 (1999; Zbl 1024.11040)].
scientific article; zbMATH DE number 2078337