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

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 (“Gp -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 Gp -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.

Shimura varieties, Newton stratification
Mathematical Subject Classification 2010
Primary: 11G18
Secondary: 11E72, 14G17
Received: 30 August 2015
Revised: 7 May 2017
Accepted: 23 October 2017
Published: 13 May 2018
Dong Uk Lee
South Korea