The Classification of the Stable Marked Reduction of Genus 2 Curves in Residue Characteristic 2
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_ | 1866911533127172096 |
|---|---|
| author | Gehrunger, Tim |
| author_facet | Gehrunger, Tim |
| contents | Consider a hyperelliptic curve of genus $2$ over a field $K$ of characteristic zero. After extending $K$ we can view it as a marked curve with its $6$ Weierstrass points. We classify the structure of the potentially stable reduction of such curves for a valuation of residue characteristic $2$. We implement this classification into a computer algebra system and compute it for a list of curves defined over $\mathbb{Q}$ with conductor at most $2^{20}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02426 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Classification of the Stable Marked Reduction of Genus 2 Curves in Residue Characteristic 2 Gehrunger, Tim Algebraic Geometry Number Theory 14H30 (14H10, 11G20) Consider a hyperelliptic curve of genus $2$ over a field $K$ of characteristic zero. After extending $K$ we can view it as a marked curve with its $6$ Weierstrass points. We classify the structure of the potentially stable reduction of such curves for a valuation of residue characteristic $2$. We implement this classification into a computer algebra system and compute it for a list of curves defined over $\mathbb{Q}$ with conductor at most $2^{20}$. |
| title | The Classification of the Stable Marked Reduction of Genus 2 Curves in Residue Characteristic 2 |
| topic | Algebraic Geometry Number Theory 14H30 (14H10, 11G20) |
| url | https://arxiv.org/abs/2507.02426 |