论文标题
时期索引问题和霍奇理论
The period-index problem and Hodge theory
论文作者
论文摘要
在第2级的Lefschetz标准猜想上，我们证明了平滑的投影品种上的Brauer类的索引将其时期的固定功率划分为平滑的家族。在另一个方向上，我们用更古典的术语重新诠释了hotchkiss的工作，这为Hodge理论的下限提供了Brauer类的索引。我们还通过任意代数封闭的基础场证明了结果的版本，并且作为应用程序构造的整体构造对整体tate猜想的新反面样本。
Conditional on the Lefschetz standard conjecture in degree 2, we prove that the index of a Brauer class on a smooth projective variety divides a fixed power of its period, uniformly in smooth families. In the other direction, we reinterpret in more classical terms recent work of Hotchkiss which gives Hodge-theoretic lower bounds on the index of Brauer classes. We also prove versions of our results over arbitrary algebraically closed base fields, and as an application construct qualitatively new counterexamples to the integral Tate conjecture.
