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Hyperelliptic curves with prescribed p-torsion

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An Erratum to this article was published on 01 September 2010

Abstract

In this paper, we show that there exist families of curves (defined over an algebraically closed field k of characteristic p>2) whose Jacobians have interesting p-torsion. For example, for every 0≤f≤g, we find the dimension of the locus of hyperelliptic curves of genus g with p-rank at most f. We also produce families of curves so that the p-torsion of the Jacobian of each fibre contains multiple copies of the group scheme α p . The method is to study curves which admit an action by (ℤ/2)n so that the quotient is a projective line. As a result, some of these families intersect the hyperelliptic locus .

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Authors and Affiliations

  1. Department of Mathematics, Columbia University, New York, NY, 10027, USA

    Darren Glass

  2. Colorado State University, 101 Weber Building, Fort Collins, CO, 80523-1874, USA

    Rachel Pries

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  1. Darren Glass
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  2. Rachel Pries
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Correspondence to Darren Glass.

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An erratum to this article is available at http://dx.doi.org/10.1007/s00229-010-0392-y.

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Glass, D., Pries, R. Hyperelliptic curves with prescribed p-torsion. manuscripta math. 117, 299–317 (2005). https://doi.org/10.1007/s00229-005-0559-0

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  • DOI: https://doi.org/10.1007/s00229-005-0559-0

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