Transcendental Brauer-Manin obstructions on singular K3 surfaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916548071915520 |
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| author | Tawfik, Mohamed Alaa Newton, Rachel |
| author_facet | Tawfik, Mohamed Alaa Newton, Rachel |
| contents | Let E and E' be elliptic curves over Q with complex multiplication by the ring of integers of an imaginary quadratic field K and let Y=Kum(ExE') be the minimal desingularisation of the quotient of ExE' by the action of -1. We study the Brauer groups of such surfaces Y and use them to furnish new examples of transcendental Brauer-Manin obstructions to weak approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00650 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Transcendental Brauer-Manin obstructions on singular K3 surfaces Tawfik, Mohamed Alaa Newton, Rachel Number Theory Algebraic Geometry 14G05 (primary), 14F22, 11G05, 14J28 (Secondary) Let E and E' be elliptic curves over Q with complex multiplication by the ring of integers of an imaginary quadratic field K and let Y=Kum(ExE') be the minimal desingularisation of the quotient of ExE' by the action of -1. We study the Brauer groups of such surfaces Y and use them to furnish new examples of transcendental Brauer-Manin obstructions to weak approximation. |
| title | Transcendental Brauer-Manin obstructions on singular K3 surfaces |
| topic | Number Theory Algebraic Geometry 14G05 (primary), 14F22, 11G05, 14J28 (Secondary) |
| url | https://arxiv.org/abs/2311.00650 |