Intermediate Jacobians and rationality over arbitrary fields
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909818991673344 |
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| author | Benoist, Olivier Wittenberg, Olivier |
| author_facet | Benoist, Olivier Wittenberg, Olivier |
| contents | We prove that a three-dimensional smooth complete intersection of two quadrics over a field k is k-rational if and only if it contains a line defined over k. To do so, we develop a theory of intermediate Jacobians for geometrically rational threefolds over arbitrary, not necessarily perfect, fields. As a consequence, we obtain the first examples of smooth projective varieties over a field k which have a k-point, and are rational over a purely inseparable field extension of k, but not over k. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_12668 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Intermediate Jacobians and rationality over arbitrary fields Benoist, Olivier Wittenberg, Olivier Algebraic Geometry We prove that a three-dimensional smooth complete intersection of two quadrics over a field k is k-rational if and only if it contains a line defined over k. To do so, we develop a theory of intermediate Jacobians for geometrically rational threefolds over arbitrary, not necessarily perfect, fields. As a consequence, we obtain the first examples of smooth projective varieties over a field k which have a k-point, and are rational over a purely inseparable field extension of k, but not over k. |
| title | Intermediate Jacobians and rationality over arbitrary fields |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1909.12668 |