Certifying nontriviality of Ceresa classes of curves
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909413016600576 |
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| author | Ellenberg, Jordan Logan, Adam Srinivasan, Padmavathi |
| author_facet | Ellenberg, Jordan Logan, Adam Srinivasan, Padmavathi |
| contents | The Ceresa cycle is a canonical algebraic $1$-cycle on the Jacobian of an algebraic curve. We construct an algorithm which, given a curve over a number field, often provides a certificate that the Ceresa cycle is non-torsion, without relying on the presence of any additional symmetries of the curve. Under the hypothesis that the Sato--Tate group is the whole of $\operatorname*{GSp}$, we prove that if the Ceresa class (the image of the Ceresa cycle in étale cohomology) is non-torsion, then the algorithm will eventually terminate with a certificate attesting to this fact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02015 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Certifying nontriviality of Ceresa classes of curves Ellenberg, Jordan Logan, Adam Srinivasan, Padmavathi Algebraic Geometry Number Theory 14C25 The Ceresa cycle is a canonical algebraic $1$-cycle on the Jacobian of an algebraic curve. We construct an algorithm which, given a curve over a number field, often provides a certificate that the Ceresa cycle is non-torsion, without relying on the presence of any additional symmetries of the curve. Under the hypothesis that the Sato--Tate group is the whole of $\operatorname*{GSp}$, we prove that if the Ceresa class (the image of the Ceresa cycle in étale cohomology) is non-torsion, then the algorithm will eventually terminate with a certificate attesting to this fact. |
| title | Certifying nontriviality of Ceresa classes of curves |
| topic | Algebraic Geometry Number Theory 14C25 |
| url | https://arxiv.org/abs/2412.02015 |