Reduction of Hyperelliptic Curves in Residue Characteristic 2
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913562048331776 |
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| author | Gehrunger, Tim Pink, Richard |
| author_facet | Gehrunger, Tim Pink, Richard |
| contents | Consider a hyperelliptic curve of genus $g$ over a field $K$ of characteristic zero. After extending $K$ we can view it as a marked curve with its $2g+2$ Weierstrass points. We present an explicit algorithm to compute the stable reduction of this marked curve for a valuation of residue characteristic $2$ over a finite extension of $K$. In the cases $g\le2$ we work out relatively simple conditions for the structure of this reduction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14214 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reduction of Hyperelliptic Curves in Residue Characteristic 2 Gehrunger, Tim Pink, Richard Algebraic Geometry Number Theory 14H30 (Primary) 14H10, 11G20 (Secondary) Consider a hyperelliptic curve of genus $g$ over a field $K$ of characteristic zero. After extending $K$ we can view it as a marked curve with its $2g+2$ Weierstrass points. We present an explicit algorithm to compute the stable reduction of this marked curve for a valuation of residue characteristic $2$ over a finite extension of $K$. In the cases $g\le2$ we work out relatively simple conditions for the structure of this reduction. |
| title | Reduction of Hyperelliptic Curves in Residue Characteristic 2 |
| topic | Algebraic Geometry Number Theory 14H30 (Primary) 14H10, 11G20 (Secondary) |
| url | https://arxiv.org/abs/2404.14214 |