Local points of twisted Mumford quotients and Shimura curves
type: Item
instance of: scholarly article
title: Local points of twisted Mumford quotients and Shimura curves
zbMATH Open document ID: 1059.14030
author: Bruce W. Jordan
author: Yakov Varshavsky
author: Ron Livné
published in: Mathematische Annalen
publication date: 2004-07-07T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 14G35
Mathematics Subject Classification ID: 11G18
Mathematics Subject Classification ID: 14G20
zbMATH DE Number: 2078337
zbMATH Keywords: Shimura variety
zbMATH Keywords: uniformisation
MaRDI profile type: Publication
full work available at URL: s00208-003-0448-3
OpenAlex ID: W2002259277
DOI: 10.1007/S00208-003-0448-3
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description: scientific article; zbMATH DE number 2078337