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Title: Newton Polygon Stratification of the Torelli Locus in Unitary Shimura Varieties
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).  more » « less
Award ID(s):
1801237
NSF-PAR ID:
10252195
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
International Mathematics Research Notices
ISSN:
1073-7928
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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