For a Shimura variety of Hodge type with hyperspecial level at a prime , the Newton stratification on its special fiber at is a stratification defined in terms of the isomorphism class of the rational Dieudonné module of parameterized abelian varieties endowed with a certain fixed set of Frobenius-invariant crystalline tensors (“-isocrystal”). There has been a conjectural group-theoretic description of the -isocrystals that are expected to show up in the special fiber. We confirm this conjecture. More precisely, for any -isocrystal that is expected to appear (in a precise sense), we construct a special point whose reduction has associated -isocrystal equal to the given one.
"Nonemptiness of Newton strata of Shimura varieties of Hodge type." Algebra Number Theory 12 (2) 259 - 283, 2018. https://doi.org/10.2140/ant.2018.12.259