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arXiv · 1801.04682

Primes dividing invariants of CM Picard curves

Pınar Kılıçer·Elisa Lorenzo García·Marco Streng
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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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Pınar Kılıçer, Elisa Lorenzo García, Marco Streng. 2018-01-15. Primes dividing invariants of CM Picard curves. https://arxiv.org/abs/1801.04682

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