2016/08/04 by Goldring, Wushi, Koskivirta, Jean-Stefan · 1 citation
#11G18 #14G35 #14K10 #20G40 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1608.01504
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.