论文标题
$ \ MATHCAL {O} $ - 无环的偶数索引
An $\mathcal{O}$-acyclic variety of even index
论文作者
论文摘要
我们给出了$ \ Mathcal {o} $ - 无环的射影射击几何连接的第一个示例，其索引不等于一个。更准确地说，我们在$ \ mathbb {p}^{1} $上构建了一个Enriques cortrfaces家族，以使任何多部分在基本$ \ Mathbb {p}^{1} $上具有甚至具有学位，并显示我们可以找到超过$ \ \ althbb {q} $的家庭。这肯定地回答了Colliot-Thélène和Voisin的问题。此外，我们的建筑提供了反述：互惠障碍所解释的哈斯原则的失败；整体霍奇猜想；和亚伯 - 雅各比地图的普遍性。
We give the first examples of $\mathcal{O}$-acyclic smooth projective geometrically connected varieties over the function field of a complex curve, whose index is not equal to one. More precisely, we construct a family of Enriques surfaces over $\mathbb{P}^{1}$ such that any multi-section has even degree over the base $\mathbb{P}^{1}$ and show moreover that we can find such a family defined over $\mathbb{Q}$. This answers affirmatively a question of Colliot-Thélène and Voisin. Furthermore, our construction provides counterexamples to: the failure of the Hasse principle accounted for by the reciprocity obstruction; the integral Hodge conjecture; and universality of Abel-Jacobi maps.
