Brauer-Manin obstruction for Wehler K3 surfaces of Markoff type
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912326955827200 |
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| author | Dao, Quang-Duc |
| author_facet | Dao, Quang-Duc |
| contents | Following recent work by E. Fuchs et al., we study the Brauer-Manin obstruction for integral points on Wehler K3 surfaces of Markoff type. In particular, we construct some families which fail the integral Hasse principle via the Brauer-Manin obstruction with some counting results of similar nature to those in previous works by Ghosh-Sarnak, Loughran-Mitankin, Colliot-Thélène-Wei-Xu. We also give some counterexamples to strong approximation (where integral points can exist) which can be explained by the Brauer-Manin obstruction, and study a few aspects of rational points on affine surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_11515 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Brauer-Manin obstruction for Wehler K3 surfaces of Markoff type Dao, Quang-Duc Number Theory Algebraic Geometry Following recent work by E. Fuchs et al., we study the Brauer-Manin obstruction for integral points on Wehler K3 surfaces of Markoff type. In particular, we construct some families which fail the integral Hasse principle via the Brauer-Manin obstruction with some counting results of similar nature to those in previous works by Ghosh-Sarnak, Loughran-Mitankin, Colliot-Thélène-Wei-Xu. We also give some counterexamples to strong approximation (where integral points can exist) which can be explained by the Brauer-Manin obstruction, and study a few aspects of rational points on affine surfaces. |
| title | Brauer-Manin obstruction for Wehler K3 surfaces of Markoff type |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2302.11515 |