Nonemptiness of Newton strata of Shimura varieties of Hodge type

Abstract

For a Shimura variety of Hodge type with hyperspecial level at a prime p, the Newton stratification on its special fiber at p is a stratification defined in terms of the isomorphism class of the rational Dieudonne module of parameterized abelian varieties endowed with a certain fixed set of Frobenius-invariant crystalline tensors (“Gℚp-isocrystal”). There has been a conjectural group-theoretic description of the F-isocrystals that are expected to show up in the special fiber. We confirm this conjecture. More precisely, for any Gℚp-isocrystal that is expected to appear (in a precise sense), we construct a special point whose reduction has associated F-isocrystal equal to the given one.