Failures of the Integral Hasse Principle for Affine Quadric Surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2016
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| _version_ | 1866912725123203072 |
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| author | Mitankin, Vladimir |
| author_facet | Mitankin, Vladimir |
| contents | Quadric hypersurfaces are well-known to satisfy the Hasse principle. However, this is no longer true in the case of the Hasse principle for integral points, where counter-examples are known to exist in dimension 1 and 2. This work explores the frequency that such counter-examples arise in a family of affine quadric surfaces defined over the integers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1604_08510 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Failures of the Integral Hasse Principle for Affine Quadric Surfaces Mitankin, Vladimir Number Theory 11D09, 11G35, 14G99 Quadric hypersurfaces are well-known to satisfy the Hasse principle. However, this is no longer true in the case of the Hasse principle for integral points, where counter-examples are known to exist in dimension 1 and 2. This work explores the frequency that such counter-examples arise in a family of affine quadric surfaces defined over the integers. |
| title | Failures of the Integral Hasse Principle for Affine Quadric Surfaces |
| topic | Number Theory 11D09, 11G35, 14G99 |
| url | https://arxiv.org/abs/1604.08510 |