A bound on the primes of bad reduction for CM curves of genus 3

    Pınar Kılıçer
    Pınar Kılıçer
    Elisa Lorenzo García
    Elisa Lorenzo García
    Rachel Newton
    Rachel Newton

    arXiv: Number Theory, 2016.

    Cited by: 10|Bibtex|Views3|

    Abstract:

    We give bounds on the primes of geometric bad reduction for curves of genus three of primitive CM type in terms of the CM orders. In the case of genus one, there are no primes of geometric bad reduction because CM elliptic curves are CM abelian varieties, which have potential good reduction everywhere. However, for genus at least two, the...More

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