Semi-integral Brauer-Manin obstruction and quadric orbifold pairs
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866908631465721856 |
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| author | Mitankin, Vladimir Nakahara, Masahiro Streeter, Sam |
| author_facet | Mitankin, Vladimir Nakahara, Masahiro Streeter, Sam |
| contents | We study local-global principles for two notions of semi-integral points, termed Campana points and Darmon points. In particular, we develop a semi-integral version of the Brauer-Manin obstruction interpolating between Manin's classical version for rational points and the integral version developed by Colliot-Thélène and Xu. We determine the status of local-global principles, and obstructions to them, in two families of orbifolds naturally associated to quadric hypersurfaces. Further, we establish a quantitative result measuring the failure of the semi-integral Brauer-Manin obstruction to account for its integral counterpart for affine quadrics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2209_15582 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Semi-integral Brauer-Manin obstruction and quadric orbifold pairs Mitankin, Vladimir Nakahara, Masahiro Streeter, Sam Number Theory Algebraic Geometry 14G12, 14G05, 11G35 We study local-global principles for two notions of semi-integral points, termed Campana points and Darmon points. In particular, we develop a semi-integral version of the Brauer-Manin obstruction interpolating between Manin's classical version for rational points and the integral version developed by Colliot-Thélène and Xu. We determine the status of local-global principles, and obstructions to them, in two families of orbifolds naturally associated to quadric hypersurfaces. Further, we establish a quantitative result measuring the failure of the semi-integral Brauer-Manin obstruction to account for its integral counterpart for affine quadrics. |
| title | Semi-integral Brauer-Manin obstruction and quadric orbifold pairs |
| topic | Number Theory Algebraic Geometry 14G12, 14G05, 11G35 |
| url | https://arxiv.org/abs/2209.15582 |