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Supersingular curves via the Shimura--Taniyama method

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arxiv 2503.04878 v2 pith:DLF22QLJ submitted 2025-03-06 math.NT math.AG

Jeremy Booher , Rachel Pries This is my paper · ORCID
classification math.NTmath.AG
keywords curvesupersingularmethodwhenabelianadmitsbranchedcharacteristic
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For a curve which admits an abelian cover of the projective line branched at three points, we study when its reduction to positive characteristic is supersingular. Using the method of Shimura and Taniyama, we give a complete classification when the genus of the curve is at most 10. The natural density of the set of primes for which this construction yields a supersingular curve is larger than expected.

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  1. The Torelli locus and Newton polygons

    math.AG 2025-08 conditional novelty 3.0 of 10

    A survey of the Torelli locus and Newton polygons that corrects a previously erroneous genus computation and thereby proves new infinite families of supersingular curves of genus δp(p−1)/2.

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