2014/08/07 by James Stankewicz, Stankewicz, James
Mathematics · #11G18 #11G30 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1408.1642
openalex publication_date 2014/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give large families of Shimura curves defined by congruence conditions, all of whose twists lack p-adic points for some p. For each such curve we give analytically large families of counterexamples to the Hasse principle via the descent (or equivalently étale Brauer-Manin) obstruction to rational points applied to étale coverings coming from the level structure. More precisely, we find infinitely many quadratic fields defined using congruence conditions such that a twist of a related Shimura curve by each of those fields violates the Hasse principle. As a minimal example, we find the twist of the genus 11 Shimura curve X143 by Q(√(-67)) and its bi-elliptic involution to violate the Hasse principle.