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Newton polygon stratification of the Torelli locus in PEL-type Shimura varieties

Li, Wanlin and Mantovan, Elena and Pries, Rachel and Tang, Yunqing (2018) Newton polygon stratification of the Torelli locus in PEL-type Shimura varieties. . (Unpublished)

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We study the intersection of the Torelli locus with the Newton polygon stratification of the modulo p reduction of certain PEL-type 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 which demonstrate unlikely intersections of the open Torelli locus with the Newton polygon stratification in Siegel modular varieties. In addition, for the twenty special PEL-type 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:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Pries, Rachel0000-0001-5987-0324
Subject Keywords:curve, cyclic cover, Jacobian, abelian variety, moduli space, Shimura variety, PEL-type, reduction, Frobenius, supersingular, Newton polygon, p-rank, Dieudonné module, p-divisible group
Classification Code:MSC10 classifications: primary 11G18, 11G20, 11M38, 14G10, 14G35; secondary 11G10, 14H10, 14H30, 14H40, 14K10
Record Number:CaltechAUTHORS:20210302-154930394
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108280
Deposited By: Tony Diaz
Deposited On:03 Mar 2021 19:23
Last Modified:15 Mar 2022 19:07

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