标志空间的分层与函性
Stratifications of flag spaces and functoriality
摘要：
我们定义商栈的“压缩标志”。它们在$G$ --由Moonen、Pink、Wedhorn和Ziegler推出的拉链--的堆叠上方形成塔。我们定义了一个分层的堆栈上的zip标志，并证明它是主要的纯，在一定的假设下，$p$。具有Hodge型Shimura簇的纤维积是Ekedahl-Van der Geer所考虑的旗空间的推广。对于大的$p$，我们证明了所有层是仿射的。本文证明了一个关于$G$ -拉链堆叠之间有限态射的纤维离散性定理。这使我们能够证明，zip分层主要是纯的所有素数$p$，霍奇型zip数据。这提供了第二个证据，完全在特征$p$，存在广义Hasse不变量的埃克达尔-奥尔特地层中的好约化志村品种的霍奇型。
英文摘要：
We define quotient stacks of "zip flags". They form towers above the stack of $G$-zips introduced by Moonen, Pink, Wedhorn and Ziegler. We define a stratification on the stack of zip flags, and prove that it is principally pure, under a certain assumption on $p$. The fiber product with a Shimura variety of Hodge-type is a generalization of flag spaces considered by Ekedahl-Van der Geer. For large $p$, we prove that all strata are affine. We prove a theorem on discreteness of fibers for finite morphisms between stacks of $G$-zips. This allows us to prove that the zip stratification is principally pure for all primes $p$, for zip data of Hodge-type. This provides a second proof, entirely in characteristic $p$, of the existence of generalized Hasse invariants for Ekedahl-Oort strata in the good reduction of Shimura varieties of Hodge-type.
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