Newton Polygons Arising for Special Families of Cyclic Covers of the Projective Line

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 $\mu$-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 $g\ge 6$, the Newton polygon with $p$-rank $g-6$ with slopes $1/6$ and $5/6$.

arXiv commentThis is a post-peer-review, pre-copyedit version of an article will appear in Research in Number Theory. The final authenticated version will be available online at: http://dx.doi.org/10.1007/s40993-018-0149-3

References in corpus (4)

• Ekedahl-Oort and Newton strata for Shimura varieties of PEL type
• The p-rank strata of the moduli space of hyperelliptic curves
• The almost product structure of Newton strata in the Deformation space of a Barsotti-Tate group with crystalline Tate tensors
• Monodromy of the p-rank strata of the moduli space of curves

Cited by in corpus (1)

• The existence of supersingular curves of genus 4 in arbitrary characteristic