An algorithm to compute Selmer groups via resolutions by permutations modules
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908325801623552 |
|---|---|
| author | Etienne, Fabrice |
| author_facet | Etienne, Fabrice |
| contents | Given a number field with absolute Galois group $\mathcal{G}$, a finite Galois module $M$, and a Selmer system $\mathcal{L}$, this article gives a method to compute Sel$_\mathcal{L}$, the Selmer group of $M$ attached to $\mathcal{L}$. First we describe an algorithm to obtain a resolution of $M$ where the morphisms are given by Hecke operators. Then we construct another group $H^1_S(\mathcal{G}, M)$ and we prove, using the properties of Hecke operators, that $H^1_S(\mathcal{G}, M)$ is a Selmer group containing Sel$_\mathcal{L}$. Then, we discuss the time complexity of this method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13506 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An algorithm to compute Selmer groups via resolutions by permutations modules Etienne, Fabrice Symbolic Computation Group Theory Number Theory Representation Theory Given a number field with absolute Galois group $\mathcal{G}$, a finite Galois module $M$, and a Selmer system $\mathcal{L}$, this article gives a method to compute Sel$_\mathcal{L}$, the Selmer group of $M$ attached to $\mathcal{L}$. First we describe an algorithm to obtain a resolution of $M$ where the morphisms are given by Hecke operators. Then we construct another group $H^1_S(\mathcal{G}, M)$ and we prove, using the properties of Hecke operators, that $H^1_S(\mathcal{G}, M)$ is a Selmer group containing Sel$_\mathcal{L}$. Then, we discuss the time complexity of this method. |
| title | An algorithm to compute Selmer groups via resolutions by permutations modules |
| topic | Symbolic Computation Group Theory Number Theory Representation Theory |
| url | https://arxiv.org/abs/2504.13506 |