#### Vol. 12, No. 2, 2018

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Nonemptiness of Newton strata of Shimura varieties of Hodge type

### Dong Uk Lee

Vol. 12 (2018), No. 2, 259–283
##### 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 Dieudonné module of parameterized abelian varieties endowed with a certain fixed set of Frobenius-invariant crystalline tensors (“${G}_{{ℚ}_{p}}$-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 ${G}_{{ℚ}_{p}}$-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.

##### Keywords
Shimura varieties, Newton stratification
##### Mathematical Subject Classification 2010
Primary: 11G18
Secondary: 11E72, 14G17