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1. CJM 2013 (vol 66 pp. 924)

Stankewicz, James
 Twists of Shimura Curves Consider a Shimura curve $X^D_0(N)$ over the rational numbers. We determine criteria for the twist by an Atkin-Lehner involution to have points over a local field. As a corollary we give a new proof of the theorem of Jordan-LivnÃ© on $\mathbf{Q}_p$ points when $p\mid D$ and for the first time give criteria for $\mathbf{Q}_p$ points when $p\mid N$. We also give congruence conditions for roots modulo $p$ of Hilbert class polynomials. Keywords:Shimura curves, complex multiplication, modular curves, elliptic curvesCategories:11G18, 14G35, 11G15, 11G10
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