Algebra & Number Theory

Nonemptiness of Newton strata of Shimura varieties of Hodge type

Dong Uk Lee

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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.

Article information

Source
Algebra Number Theory, Volume 12, Number 2 (2018), 259-283.

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1527040844

Digital Object Identifier
doi:10.2140/ant.2018.12.259

Mathematical Reviews number (MathSciNet)
MR3803703

Zentralblatt MATH identifier
06880888

Subjects
Primary: 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35]
Secondary: 11E72: Galois cohomology of linear algebraic groups [See also 20G10] 14G17: Positive characteristic ground fields

Keywords
Shimura varieties Newton stratification

Citation

Lee, Dong Uk. Nonemptiness of Newton strata of Shimura varieties of Hodge type. Algebra Number Theory 12 (2018), no. 2, 259--283. doi:10.2140/ant.2018.12.259. https://projecteuclid.org/euclid.ant/1527040844


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