On Birch and Swinnerton-Dyer's cubic surfaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2015
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| _version_ | 1866917679858712576 |
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| author | West, Mckenzie |
| author_facet | West, Mckenzie |
| contents | In a 1975 paper of Birch and Swinnerton-Dyer, a number of explicit norm form cubic surfaces are shown to fail the Hasse Principle. They make a correspondence between this failure and the Brauer--Manin obstruction, recently discovered by Manin. We generalize their work, making use of modern computer algebra software to show that a larger set of cubic surfaces have a Brauer--Manin obstruction to the Hasse principle, thus verifying the Colliot-Thélène--Sansuc conjecture for infinitely many cubic surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1510_03769 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | On Birch and Swinnerton-Dyer's cubic surfaces West, Mckenzie Number Theory Algebraic Geometry 14G05, 14F22, 11G35 In a 1975 paper of Birch and Swinnerton-Dyer, a number of explicit norm form cubic surfaces are shown to fail the Hasse Principle. They make a correspondence between this failure and the Brauer--Manin obstruction, recently discovered by Manin. We generalize their work, making use of modern computer algebra software to show that a larger set of cubic surfaces have a Brauer--Manin obstruction to the Hasse principle, thus verifying the Colliot-Thélène--Sansuc conjecture for infinitely many cubic surfaces. |
| title | On Birch and Swinnerton-Dyer's cubic surfaces |
| topic | Number Theory Algebraic Geometry 14G05, 14F22, 11G35 |
| url | https://arxiv.org/abs/1510.03769 |