Primes Dividing Invariants of CM Picard Curves

Kılıçer, P., García, E. L. & Streng, M., 15-Nov-2018, In : Canadian journal of mathematics-Journal canadien de mathematiques. p. 1-25

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  • Primes Dividing Invariants of CM PicardCurves

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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.
Original languageEnglish
Pages (from-to)1-25
JournalCanadian journal of mathematics-Journal canadien de mathematiques
Publication statusE-pub ahead of print - 15-Nov-2018


  • math.NT, math.AG, 14H45, 14K22, 11H06, 14G50, 14H40, 14Q05

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