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Preprints, Working Papers, ... (Preprint) Year : 2023

Explicit Riemann-Roch spaces in the Hilbert class field

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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Dates and versions

hal-04219975 , version 1 (14-12-2023)

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Jean-Marc Couveignes, Jean Gasnier. Explicit Riemann-Roch spaces in the Hilbert class field. 2023. ⟨hal-04219975⟩
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