论文标题
派生的$ f $ -zips
Derived $F$-zips
论文作者
论文摘要
我们将$ f $ zips的派生版本定义为派生的$ f $ -zip，以实现积极特征的任何适当，平滑的形态。我们分析了衍生的$ f $ zips和某些替代的堆栈。我们与经典理论建立了联系，并研究试图概括该理论以衍生$ g $ zips和衍生的$ f $ zips时出现的问题。作为一个应用程序，我们查看Enriques-Surfaces，并通过关联的派生$ F $ -ZIPS分析Enriques-Surfaces的模量堆栈的几何形状。由于特征性的$ 2 $具有不良的hodge-de hodge-de rham光谱序列，因此提供了一种新方法，以前无法通过$ f $ zips的经典理论获得。
We define derived versions of $F$-zips and associate a derived $F$-zip to any proper, smooth morphism of schemes in positive characteristic. We analyze the stack of derived $F$-zips and certain substacks. We make a connection to the classical theory and look at problems that arise when trying to generalize the theory to derived $G$-zips and derived $F$-zips associated to lci morphisms. As an application, we look at Enriques-surfaces and analyze the geometry of the moduli stack of Enriques-surfaces via the associated derived $F$-zips. As there are Enriques-surfaces in characteristic $2$ with non-degenerate Hodge-de Rham spectral sequence, this gives a new approach, which could previously not be obtained by the classical theory of $F$-zips.
