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Newton Polygon Stratification of the Torelli Locus in Unitary Shimura Varieties

Li, Wanlin and Mantovan, Elena and Pries, Rachel and Tang, Yunqing (2022) Newton Polygon Stratification of the Torelli Locus in Unitary Shimura Varieties. International Mathematics Research Notices, 2022 (9). pp. 6464-6511. ISSN 1073-7928. doi:10.1093/imrn/rnaa306. https://resolver.caltech.edu/CaltechAUTHORS:20220623-483313800

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Abstract

We study the intersection of the Torelli locus with the Newton polygon stratification of the modulo p reduction of certain Shimura varieties. We develop a clutching method to show that the intersection of the open Torelli locus with some Newton polygon strata is non-empty. This allows us to give a positive answer, under some compatibility conditions, to a question of Oort about smooth curves in characteristic p whose Newton polygons are an amalgamate sum. As an application, we produce infinitely many new examples of Newton polygons that occur for smooth curves that are cyclic covers of the projective line. Most of these arise in inductive systems that demonstrate unlikely intersections of the open Torelli locus with the Newton polygon stratification in Siegel modular varieties. In addition, for the 20 special Shimura varieties found in Moonen’s work, we prove that all Newton polygon strata intersect the open Torelli locus (if p>>0 in the supersingular cases).


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1093/imrn/rnaa306DOIArticle
ORCID:
AuthorORCID
Pries, Rachel0000-0001-5987-0324
Additional Information:© The Author(s) 2020. Published by Oxford University Press. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model). Received: 22 August 2019; Revision received: 31 July 2020; Accepted: 06 October 2020; Published: 09 December 2020. We thank the Banff International Research Station for hosting Women in Numbers 4, the American Institute of Mathematics for supporting our square proposal, and anonymous referees for valuable suggestions. This work was partially supported by the National Science Foundation [grants DMS-15-02227 and DMS-19-01819 to R.P.; grant DMS-18-01237 to Y.T.].
Funders:
Funding AgencyGrant Number
NSFDMS-15-02227
NSFDMS-19-01819
NSFDMS-18-01237
Issue or Number:9
DOI:10.1093/imrn/rnaa306
Record Number:CaltechAUTHORS:20220623-483313800
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220623-483313800
Official Citation:Wanlin Li, Elena Mantovan, Rachel Pries, Yunqing Tang, Newton Polygon Stratification of the Torelli Locus in Unitary Shimura Varieties, International Mathematics Research Notices, Volume 2022, Issue 9, May 2022, Pages 6464–6511, https://doi.org/10.1093/imrn/rnaa306
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115248
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:24 Jun 2022 22:54
Last Modified:28 Jun 2022 19:23

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