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arXiv · 2409.15580

Prym varieties and cubic threefolds over $\mathbb{Z}$

Tudor Ciurca
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Abstract

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.

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Tudor Ciurca. 2024-09-23. Prym varieties and cubic threefolds over $\mathbb{Z}$. https://arxiv.org/abs/2409.15580

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