Primes dividing invariants of CM Picard curves
Number Theory
2018-09-18 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1801.04682,
title = {Primes dividing invariants of CM Picard curves},
author = {Pınar Kılıçer and Elisa Lorenzo García and Marco Streng},
journal= {arXiv preprint arXiv:1801.04682},
year = {2018}
}