Rational and integral points on Markoff-type K3 surfaces
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916695597121536 |
|---|---|
| author | Dao, Quang-Duc |
| author_facet | Dao, Quang-Duc |
| contents | Following recent works by E. Fuchs et al. and by the author, we study rational and integral points on Markoff-type K3 (MK3) surfaces, i.e., Wehler K3 surfaces of Markoff type. In particular, we construct a family of MK3 surfaces which have a Zariski dense set of rational points but fail the integral Hasse principle due to the Brauer-Manin obstruction and provide some counting results for this family. We also give some remarks on Brauer groups, Picard groups, and failure of strong approximation on MK3 surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10992 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rational and integral points on Markoff-type K3 surfaces Dao, Quang-Duc Number Theory Algebraic Geometry 11G35, 14G12, 11D41, 14F22 Following recent works by E. Fuchs et al. and by the author, we study rational and integral points on Markoff-type K3 (MK3) surfaces, i.e., Wehler K3 surfaces of Markoff type. In particular, we construct a family of MK3 surfaces which have a Zariski dense set of rational points but fail the integral Hasse principle due to the Brauer-Manin obstruction and provide some counting results for this family. We also give some remarks on Brauer groups, Picard groups, and failure of strong approximation on MK3 surfaces. |
| title | Rational and integral points on Markoff-type K3 surfaces |
| topic | Number Theory Algebraic Geometry 11G35, 14G12, 11D41, 14F22 |
| url | https://arxiv.org/abs/2504.10992 |