On the Hasse principle for Shimura curves
On the Hasse principle for Shimura curves
复制标题
关于 Shimura 曲线的 Hasse 原理
DOI：
10.1007/s11856-009-0053-6
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发表时间：
2005
影响因子：
1
通讯作者：
P. L. Clark
中科院分区：
文献类型：
--
作者：
P. L. Clark
Let C be an algebraic curve defined over a number field K, of positive genus and without K-rational points. We conjecture that there exists some extension field L over which C has points everywhere locally but not globally. We show that our conjecture holds for all but finitely many Shimura curves of the form X0D (N)/ℚ or X1D (N)/ℚ, where D > 1 and N are coprime squarefree positive integers. The proof uses a variation on a theorem of Frey, a gonality bound of Abramovich, and an analysis of local points of small degree.
