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Primes Dividing Invariants of CM Picard Curves

  • Pınar Kılıçer (a1), Elisa Lorenzo García (a2) and Marco Streng (a3)

Abstract

We give a bound on the primes dividing the denominators of invariants of Picard curves of genus 3 with complex multiplication. Unlike earlier bounds in genus 2 and 3, our bound is based, not on bad reduction of curves, but on a very explicit type of good reduction. This approach simultaneously yields a simplification of the proof and much sharper bounds. In fact, unlike all previous bounds for genus 3, our bound is sharp enough for use in explicit constructions of Picard curves.

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Copyright

Footnotes

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Author E. L. G. was partially supported by a project PEPS-Jeunes Chercheur-e-s - 2017. Author P. K. was partially supported by DFG priority project SPP 1489.

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References

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Primes Dividing Invariants of CM Picard Curves

  • Pınar Kılıçer (a1), Elisa Lorenzo García (a2) and Marco Streng (a3)

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