Algebra & Number Theory
- Algebra Number Theory
- Volume 12, Number 2 (2018), 259-283.
Nonemptiness of Newton strata of Shimura varieties of Hodge type
For a Shimura variety of Hodge type with hyperspecial level at a prime , the Newton stratification on its special fiber at 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 (“-isocrystal”). There has been a conjectural group-theoretic description of the -isocrystals that are expected to show up in the special fiber. We confirm this conjecture. More precisely, for any -isocrystal that is expected to appear (in a precise sense), we construct a special point whose reduction has associated -isocrystal equal to the given one.
Algebra Number Theory, Volume 12, Number 2 (2018), 259-283.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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