Irreducibility of the Siegel moduli spaces with parahoric level structure

الأصل · EN

We prove that the moduli space Ag,ᵧ₀₍ₚ₎⊗ Fₚ of principally polarized abelian varieties of dimension g with a Γ₀(p)-level structure in characteristic p has 2ᵍ irreducible components.The cases of other parahoric level structures are also considered.