Proceedings/Recueil Des Communications Contemporary mathematics Année : 2026

Explicit Riemann-Roch spaces in the Hilbert class field

Résumé

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.

Fichier principal
Vignette du fichier
couveignes-gasnier.pdf (452.98 Ko) Télécharger le fichier

Dates et versions

hal-04219975 , version 1 (14-12-2023)
hal-04219975 , version 2 (22-09-2024)

Licence

Identifiants

Citer

Jean-Marc Couveignes, Jean Gasnier. Explicit Riemann-Roch spaces in the Hilbert class field. Arithmetic, geometry, cryptography and coding theory, Jun 2023, MARSEILLE (FRANCE), France. Contemporary mathematics, 832, American mathematical society, 2026, 978-1-4704-7685-4. ⟨hal-04219975v2⟩
307 Consultations
400 Téléchargements

Altmetric

Partager

  • More