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arXiv · 2012.08705

The $a$-number, $p$-rank and Cartier points of genus 4 curves

Catalina Camacho-Navarro
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Abstract

We study genus $4$ curves over finite fields and two invariants of the $p$-torsion part of their Jacobians: the $a$-number ($a$) and $p$-rank ($f$). We collect and analyze statistical data of curves over $\mathbb{F}_p$ for $p=3,5,7,11$ and their invariants. Then, we study the existence of Cartier points, which are also related to the structure of $J[p]$. For curves with $0\leq a<g$, the number of Cartier points is bounded, and it depends on $a$ and $f$.

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Catalina Camacho-Navarro. 2020-12-16. The $a$-number, $p$-rank and Cartier points of genus 4 curves. https://arxiv.org/abs/2012.08705

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