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arXiv · 2012.08683

Recovering affine curves over finite fields from $L$-functions

Jeremy Booher·José Felipe Voloch
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Abstract

Let $K$ be the function field of a curve over a finite field of odd characteristic. We investigate using $L$-functions of Galois extensions of $K$ to effectively recover $K$. When $K$ is the function field of the projective line with four rational points removed, we show how to use $L$-functions of a ray class field to effectively recover the removed points up to automorphisms of the projective line. When $K$ is the function field of a plane curve, we show how to effectively recover the equation of that curve using $L$-functions of Artin-Schreier extensions of $K$.

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BibTeXRIS

Jeremy Booher, José Felipe Voloch. 2020-12-16. Recovering affine curves over finite fields from $L$-functions. https://doi.org/10.2140/pjm.2021.314.1

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