论文标题
旋转派生类别和周期索引问题的霍奇理论
Hodge theory of twisted derived categories and the period-index problem
论文作者
论文摘要
我们研究了扭曲的衍生类别的霍奇理论及其与时期指数问题的关系。我们的主要贡献是开发了一种扭曲的Mukai结构理论，用于关于任意平滑的合适品种和家庭中拓扑琐碎的brauer类。作为应用程序，我们构建了hodge类，其代数将暗示周期索引的界限；在Severi-Brauer品种上构建新的反示例；并证明了DeLigne-Mumford表面的派生类别的整体Hodge猜想。
We study the Hodge theory of twisted derived categories and its relation to the period-index problem. Our main contribution is the development of a theory of twisted Mukai structures for topologically trivial Brauer classes on arbitrary smooth proper varieties and in families. As applications, we construct Hodge classes whose algebraicity would imply period-index bounds; construct new counterexamples to the integral Hodge conjecture on Severi-Brauer varieties; and prove the integral Hodge conjecture for derived categories of Deligne-Mumford surfaces.
