非分裂纤维少的纤维化的有理点
Rational points on fibrations with few non-split fibres
摘要：
我们重新审视抽象框架的纤维化方法生产有理点的纤维化的全空间上的投影线。通过微调其对外部算术代数的依赖性，我们使该方法无条件时，非分裂轨迹的程度是$\leq 2$，以及在各种情况下，它是$3$。我们也能够获得改善的结果，在该制度下，是有条件的访问Schinzel的假设，纳入其中，第一次，一种技术，由于Harari控制Brauer-Manin阻塞的家庭。
英文摘要：
We revisit the abstract framework underlying the fibration method for producing rational points on the total space of fibrations over the projective line. By fine-tuning its dependence on external arithmetic conjectures, we render the method unconditional when the degree of the non-split locus is $\leq 2$, as well as in various instances where it is $3$. We are also able to obtain improved results in the regime that is conditionally accessible under Schinzel's hypothesis, by incorporating into it, for the first time, a technique due to Harari for controlling the Brauer--Manin obstruction in families.
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