The product structure of Newton strata in the good reduction of Shimura varieties of Hodge type

Hamacher, Paul

doi:10.1090/jag/732

Author: Paul Hamacher
Journal: J. Algebraic Geom. 28 (2019), 721-749
DOI: https://doi.org/10.1090/jag/732
Published electronically: July 11, 2019
MathSciNet review: 3994311
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Abstract | References | Additional Information

Abstract: We construct a generalisation of Mantovan’s almost product structure to Shimura varieties of Hodge type with hyperspecial level structure at $p$ and deduce that the perfection of the Newton strata are proétale locally isomorphic to the perfection of the product of a central leaf and a Rapoport-Zink space. The almost product formula can be extended to obtain an analogue of Caraiani and Scholze’s generalisation of the almost product structure for Shimura varieties of Hodge type.

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Additional Information

Paul Hamacher
Affiliation: Zentrum Mathematik - M11, Technische Universiät München, Boltzmannstraße 3, 85748 Garching bei München, Germany
MR Author ID: 1048654
Email: hamacher@ma.tum.de

Received by editor(s): October 6, 2017
Received by editor(s) in revised form: May 18, 2018, and August 30, 2018
Published electronically: July 11, 2019
Additional Notes: The author was partially supported by the ERC starting grant 277889 “Moduli spaces of local $G$-shtukas”.
Article copyright: © Copyright 2019 University Press, Inc.