Newton polygons arising from special families of cyclic covers of the projective line View Full Text


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Article Info

DATE

2019-03

AUTHORS

Wanlin Li, Elena Mantovan, Rachel Pries, Yunqing Tang

ABSTRACT

By a result of Moonen, there are exactly 20 positive-dimensional families of cyclic covers of the projective line for which the Torelli image is open and dense in the associated Shimura variety. For each of these, we compute the Newton polygons, and the μ-ordinary Ekedahl–Oort type, occurring in the characteristic p reduction of the Shimura variety. We prove that all but a few of the Newton polygons appear on the open Torelli locus. As an application, we produce multiple new examples of Newton polygons and Ekedahl–Oort types of Jacobians of smooth curves in characteristic p. Under certain congruence conditions on p, these include: the supersingular Newton polygon for genus 5, 6, 7; fourteen new non-supersingular Newton polygons for genus 5–7; eleven new Ekedahl–Oort types for genus 4–7 and, for all g≥6, the Newton polygon with p-rank g-6 with slopes 1 / 6 and 5 / 6. More... »

PAGES

12

References to SciGraph publications

  • 2003-02. On the existence of F-crystals in COMMENTARII MATHEMATICI HELVETICI
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  • 2017-03. Stratifications in the reduction of Shimura varieties in MANUSCRIPTA MATHEMATICA
  • 2005-07. Hyperelliptic curves with prescribed p-torsion in MANUSCRIPTA MATHEMATICA
  • 1997-12. Isocrystals with additional structure. II in COMPOSITIO MATHEMATICA
  • 2001-05. The p-Rank of Ramified Covers of Curves in COMPOSITIO MATHEMATICA
  • 2011-06. The supersingular locus of the Shimura variety of GU(1,n−1) II in INVENTIONES MATHEMATICAE
  • 2017-12. The almost product structure of Newton strata in the Deformation space of a Barsotti–Tate group with crystalline Tate tensors in MATHEMATISCHE ZEITSCHRIFT
  • 1995. Boundary behaviour of Hurwitz schemes in THE MODULI SPACE OF CURVES
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    http://scigraph.springernature.com/pub.10.1007/s40993-018-0149-3

    DOI

    http://dx.doi.org/10.1007/s40993-018-0149-3

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