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.
|Number of pages||25|
|Journal||Canadian journal of mathematics-Journal canadien de mathematiques|
|Early online date||15-Nov-2018|
|Publication status||Published - Apr-2020|
- 14H45, 14K22, 11H06, 14G50, 14H40, 14Q05