Non-simple abelian varieties in a family: Geometric and analytic approaches

Jordan S. Ellenberg, Christian Elsholtz, Chris Hall, Emmanuel Kowalski

    Research output: Contribution to journalArticleResearchpeer-review

    Abstract

    We consider, in the special case of certain one-parameter families of Jacobians of curves defined over a number field, the problem of how the property that the generic fiber of such a family is absolutely simple 'spreads' to other fibers. We show that this question can be approached using arithmetic geometry or with more analytic methods based on sieve theory. In the first setting, non-trivial group-theoretic information is needed, while the version of the sieve we use is also of independent interest.

    Original languageEnglish
    Pages (from-to)135-154
    Number of pages20
    JournalJournal of the London Mathematical Society
    Volume80
    Issue number1
    DOIs
    Publication statusPublished - Aug 2009

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    Sieve
    Abelian Variety
    Fiber
    Number field
    Curve
    Family

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Non-simple abelian varieties in a family : Geometric and analytic approaches. / Ellenberg, Jordan S.; Elsholtz, Christian; Hall, Chris; Kowalski, Emmanuel.

    In: Journal of the London Mathematical Society, Vol. 80, No. 1, 08.2009, p. 135-154.

    Research output: Contribution to journalArticleResearchpeer-review

    Ellenberg, Jordan S. ; Elsholtz, Christian ; Hall, Chris ; Kowalski, Emmanuel. / Non-simple abelian varieties in a family : Geometric and analytic approaches. In: Journal of the London Mathematical Society. 2009 ; Vol. 80, No. 1. pp. 135-154.
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