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arXiv · 2309.06754

Explicit Riemann-Roch spaces in the Hilbert class field

Jean-Marc Couveignes·Jean Gasnier
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Abstract

Let $\mathbf K$ be a finite field, $X$ and $Y$ two curves over $\mathbf K$, and $Y\rightarrow X$ an unramified abelian cover with Galois group $G$. Let $D$ be a divisor on $X$ and $E$ its pullback on $Y$. Under mild conditions the linear space associated with $E$ is a free ${\mathbf K}[G]$-module. We study the algorithmic aspects and applications of these modules.

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Jean-Marc Couveignes, Jean Gasnier. 2023-09-13. Explicit Riemann-Roch spaces in the Hilbert class field. https://arxiv.org/abs/2309.06754

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