论文标题
Brauer和Etale同型障碍
Brauer and Etale Homotopy Obstructions to Rational Points on Open Covers
论文作者
论文摘要
在2010年，Poonen举例说明了当地全球原则失败的第一个例子，Skorobogatov的典型布劳尔 - 曼宁障碍物无法解释。在此示例中，我们表明，Brauer-Manin障碍物在任何想象中的二次或完全真实的领域都在足够细的Zariski开放盖上检测到理性点不存在。我们提供了一些证据，说明为什么预期这种情况会在任何数字字段上更普遍地发生，其中一些与阿纳贝尔几何形状中的部分猜想有关。然后，我们证明了使用Harpaz和第二作者使用étale同型障碍物在品种纤维中的行为。最终，我们使用该结果和其他技术来进一步分析Poonen的榜样，鉴于我们的一般结果。
In 2010, Poonen gave the first example of failure of the local-global principle that cannot be explained by Skorobogatov's étale Brauer-Manin obstruction. Motivated by this example, we show that the Brauer-Manin obstruction detects non-existence of rational points on a sufficiently fine Zariski open cover of any variety over an imaginary quadratic or totally real field. We provide some evidence for why this is expected to happen more generally over any number field, some of which relates to the section conjecture in anabelian geometry. We then prove a result about the behavior of the étale Brauer obstruction in fibrations of varieties using the étale homotopy obstruction of Harpaz and the second author. We finally use that result and other techniques to further analyze Poonen's example in light of our general results.
