Explicit Riemann-Roch spaces in the Hilbert class field
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913510790791168 |
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| author | Couveignes, Jean-Marc Gasnier, Jean |
| author_facet | Couveignes, Jean-Marc Gasnier, Jean |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06754 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Explicit Riemann-Roch spaces in the Hilbert class field Couveignes, Jean-Marc Gasnier, Jean Number Theory 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. |
| title | Explicit Riemann-Roch spaces in the Hilbert class field |
| topic | Number Theory |
| url | https://arxiv.org/abs/2309.06754 |