Geodesic
Primes Dividing Invariants of CM Picard Curves
Canadian journal of mathematics, Tome 72 (2020) no. 2, pp. 480-504

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DOI

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.
DOI : 10.4153/S0008414X18000111
Mots-clés : Picard curve, curve invariant, complex multiplciation, Hilbert class polynomial, bad reduction 
Kılıçer, Pınar; García, Elisa Lorenzo; Streng, Marco. Primes Dividing Invariants of CM Picard Curves. Canadian journal of mathematics, Tome 72 (2020) no. 2, pp. 480-504. doi: 10.4153/S0008414X18000111
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     title = {Primes {Dividing} {Invariants} of {CM} {Picard} {Curves}},
     journal = {Canadian journal of mathematics},
     pages = {480--504},
     year = {2020},
     volume = {72},
     number = {2},
     doi = {10.4153/S0008414X18000111},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X18000111/}
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