[
    {
        "id": "authors:yk4qj-72d73",
        "collection": "authors",
        "collection_id": "yk4qj-72d73",
        "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190801-153624143",
        "type": "book_section",
        "title": "Newton Polygons of Cyclic Covers of the Projective Line Branched at Three Points",
        "book_title": "Research Directions in Number Theory - Women in Numbers IV",
        "author": [
            {
                "family_name": "Li",
                "given_name": "Wanlin",
                "clpid": "Li-Wanlin"
            },
            {
                "family_name": "Mantovan",
                "given_name": "Elena",
                "clpid": "Mantovan-E"
            },
            {
                "family_name": "Pries",
                "given_name": "Rachel",
                "clpid": "Pries-R"
            },
            {
                "family_name": "Tang",
                "given_name": "Yunqing",
                "clpid": "Tang-Yunqing"
            }
        ],
        "contributor": [
            {
                "family_name": "Balakrishnan",
                "given_name": "Jennifer S.",
                "clpid": "Balakrishnan-J-S"
            },
            {
                "family_name": "Folsom",
                "given_name": "Amanda",
                "clpid": "Folsom-A"
            },
            {
                "family_name": "Lal\u00edn",
                "given_name": "Matilde",
                "clpid": "Lal\u00edn-M"
            },
            {
                "family_name": "Manes",
                "given_name": "Michelle",
                "clpid": "Manes-M"
            }
        ],
        "abstract": "We review the Shimura\u2013Taniyama 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\u2009\u2264\u2009g\u2009\u2264\u200911; nine non-supersingular Newton polygons with p-rank 0 with 4\u2009\u2264\u2009g\u2009\u2264\u200911; and, for all g\u2009\u2265\u20095, the Newton polygon with p-rank g\u2009\u2212\u20095 having slopes 1\u22155 and 4\u22155.",
        "doi": "10.1007/978-3-030-19478-9_5",
        "isbn": "978-3-030-19477-2",
        "publisher": "Springer",
        "place_of_publication": "Cham",
        "publication_date": "2019-08-02",
        "pages": "115-132"
    }
]