Prym varieties and cubic threefolds over $\mathbb{Z}$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909323918049280 |
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| author | Ciurca, Tudor |
| author_facet | Ciurca, Tudor |
| contents | We develop a theory of Prym varieties and cubic threefolds over fields of characteristic $2$. As an application, we prove that smooth cubic threefolds are non-rational over an arbitrary field and solve a conjecture of Deligne regarding arithmetic Torelli maps. We also prove the Torelli theorem for cubic threefolds over arbitrary fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15580 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Prym varieties and cubic threefolds over $\mathbb{Z}$ Ciurca, Tudor Algebraic Geometry 14H40, 14C25, 14D23, 14E08 We develop a theory of Prym varieties and cubic threefolds over fields of characteristic $2$. As an application, we prove that smooth cubic threefolds are non-rational over an arbitrary field and solve a conjecture of Deligne regarding arithmetic Torelli maps. We also prove the Torelli theorem for cubic threefolds over arbitrary fields. |
| title | Prym varieties and cubic threefolds over $\mathbb{Z}$ |
| topic | Algebraic Geometry 14H40, 14C25, 14D23, 14E08 |
| url | https://arxiv.org/abs/2409.15580 |