On the slope stratification of certain Shimura varieties

Details On the slope stratification of certain Shimura varieties On the slope stratification of certain Shimura varieties

2004-11-17

arxiv.org/abs/math/0411373v2

Mathematics

Algebraic Geometry

Revised version, 14 pages

Scientific paper

In this paper we study the slope stratification on the good reduction of the type C family Shimura varieties. We show that there is an open dense subset $U$ of the moduli space such that any point in $U$ can be deformed to a point with a given lower {\it admissible} Newton polygon. For the Siegel moduli spaces, this is obtained by F. Oort which plays an important role in his proof of the strong Grothendieck conjecture concerning the slope stratification. We also investigate the $p$-divisible groups and their isogeny classes arising from the abelian varieties in question.

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