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2018 Nonemptiness of Newton strata of Shimura varieties of Hodge type
Dong Uk Lee
Algebra Number Theory 12(2): 259-283 (2018). 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 (“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.

Citation

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Dong Uk Lee. "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

Information

Received: 30 August 2015; Revised: 7 May 2017; Accepted: 23 October 2017; Published: 2018
First available in Project Euclid: 23 May 2018

zbMATH: 06880888
MathSciNet: MR3803703
Digital Object Identifier: 10.2140/ant.2018.12.259

Subjects:
Primary: 11G18
Secondary: 11E72, 14G17

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.12 • No. 2 • 2018
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