Le principe de Hasse pour les intersections de deux quadriques dans $\mathbb{P}^7$
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910473415294976 |
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| author | Molyakov, Alexander |
| author_facet | Molyakov, Alexander |
| contents | We prove the Hasse principle for a smooth proper model of a geometrically integral non-conical intersection of two quadrics in the projective space of dimension 7 over a number field. This result generalizes the result of Heath-Brown who established the statement in the smooth case. Our argument is built upon the ideas of Colliot-Thélène and the fibration method for zero-cycles in the form of Harpaz-Wittenberg. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00313 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Le principe de Hasse pour les intersections de deux quadriques dans $\mathbb{P}^7$ Molyakov, Alexander Algebraic Geometry 14G12, 14G05, 14G20, 14G25 We prove the Hasse principle for a smooth proper model of a geometrically integral non-conical intersection of two quadrics in the projective space of dimension 7 over a number field. This result generalizes the result of Heath-Brown who established the statement in the smooth case. Our argument is built upon the ideas of Colliot-Thélène and the fibration method for zero-cycles in the form of Harpaz-Wittenberg. |
| title | Le principe de Hasse pour les intersections de deux quadriques dans $\mathbb{P}^7$ |
| topic | Algebraic Geometry 14G12, 14G05, 14G20, 14G25 |
| url | https://arxiv.org/abs/2305.00313 |