关于判别式$pq$的Shimura过程的Atkin-Lehner定理的几点思考
Points rationnels sur les quotients d'Atkin-Lehner de courbes de Shimura de discriminant $pq$
摘要：
设$p$和$q$是两个不同的素数，$X^{pq}/w_q$是判别式$pq$的Shimura曲线与Atkin-Lehner对合$w_q$的商。我们描述了一种方法来验证在广泛的一般性的标准父母和Yafaev证明，如果$p$和$q$满足一些显式的同余条件，被称为条件的非分歧的情况下Ogg，如果$p$是足够大的相比，$q$，那么商$X^{pq}/w_q$没有有理点，除了可能的特殊点。
英文摘要：
Let $p$ and $q$ be two distinct prime numbers, and $X^{pq}/w_q$ be the quotient of the Shimura curve of discriminant $pq$ by the Atkin-Lehner involution $w_q$. We describe a way to verify in wide generality a criterion of Parent and Yafaev to prove that if $p$ and $q$ satisfy some explicite congruence conditions, known as the conditions of the non ramified case of Ogg, and if $p$ is large enough compared to $q$, then the quotient $X^{pq}/w_q$ has no rational point, except possibly special points.
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