Supersingular curves via the Shimura--Taniyama method
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909619376357376 |
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| author | Booher, Jeremy Pries, Rachel |
| author_facet | Booher, Jeremy Pries, Rachel |
| contents | For a curve which admits an abelian cover of the projective line branched at three points, we study when its reduction to positive characteristic is supersingular. Using the method of Shimura and Taniyama, we give a complete classification when the genus of the curve is at most 10. The natural density of the set of primes for which this construction yields a supersingular curve is larger than expected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04878 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Supersingular curves via the Shimura--Taniyama method Booher, Jeremy Pries, Rachel Number Theory Algebraic Geometry 11G20, 11M38, 14G10, 14H10, 14H40 For a curve which admits an abelian cover of the projective line branched at three points, we study when its reduction to positive characteristic is supersingular. Using the method of Shimura and Taniyama, we give a complete classification when the genus of the curve is at most 10. The natural density of the set of primes for which this construction yields a supersingular curve is larger than expected. |
| title | Supersingular curves via the Shimura--Taniyama method |
| topic | Number Theory Algebraic Geometry 11G20, 11M38, 14G10, 14H10, 14H40 |
| url | https://arxiv.org/abs/2503.04878 |