Nonemptiness of Newton strata of Shimura varieties of Hodge type

Lee, Dong Uk

doi:10.2140/ant.2018.12.259

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Nonemptiness of Newton strata of Shimura varieties of Hodge type

Dong Uk Lee

Vol. 12 (2018), No. 2, 259–283

DOI: 10.2140/ant.2018.12.259

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

Milestones

Received: 30 August 2015

Revised: 7 May 2017

Accepted: 23 October 2017

Published: 13 May 2018

Authors

Dong Uk Lee
Seoul South Korea

Vol. 12, No. 2, 2018