Irreducibility and p-adic monodromies on the Siegel moduli spaces

Mathematics – Number Theory

Scientific paper

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Revised version, 30 pages

Scientific paper

We generalize the surjectivity result of the $p$-adic monodromy for the ordinary locus of a Siegel moduli space by Faltings and Chai (independently by Ekedahl) to that for any $p$-rank stratum. We discuss irreducibility and connectedness of some $p$-rank strata of the moduli spaces with parahoric level structure. Finer results are obtained on the Siegel 3-fold with Iwahori level structure.

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