@inbook{da24983be37b44528012e334261a0ead,

title = "Newton Polygons of Cyclic Covers of the Projective Line Branched at Three Points",

abstract = "We review the Shimura–Taniyama method for computing the Newton polygon of an abelian variety with complex multiplication. We apply this method to cyclic covers of the projective line branched at three points. As an application, we produce multiple new examples of Newton polygons that occur for Jacobians of smooth curves in characteristic p. Under certain congruence conditions on p, these include: the supersingular Newton polygon for each genus g with 4 ≤ g ≤ 11; nine non-supersingular Newton polygons with p-rank 0 with 4 ≤ g ≤ 11; and, for all g ≥ 5, the Newton polygon with p-rank g − 5 having slopes 1∕5 and 4∕5.",

keywords = "Abelian variety, Complex multiplication, Curve, Cyclic cover, Dieudonn{\'e} module, Jacobian, Moduli space, Newton polygon, Reduction, Shimura–Taniyama method, Supersingular, p-divisible group, p-rank",

author = "Wanlin Li and Elena Mantovan and Rachel Pries and Yunqing Tang",

note = "Funding Information: This project began at the Women in Numbers 4 workshop at the Banff International Research Station. Pries was partially supported by NSF grant DMS-15-02227. We thank the referee for the valuable feedback and comments.",

year = "2019",

doi = "10.1007/978-3-030-19478-9_5",

language = "English (US)",

series = "Association for Women in Mathematics Series",

publisher = "Springer",

pages = "115--132",

booktitle = "Association for Women in Mathematics Series",

}