Brauer groups of certain affine cubic surfaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866918177061994496 |
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| author | Alfaraj, Abdulmuhsin |
| author_facet | Alfaraj, Abdulmuhsin |
| contents | We study the Brauer groups of affine surfaces that are complements of singular hyperplane sections of smooth cubic surfaces over a field $k$ of characteristic $0$. We determine the Brauer group over the algebraic closure as a Galois module for all the possible singular hyperplane sections. For the case when the hyperplane section is geometrically the union of three lines, we give explicit examples where transcendental elements of order $2$ and $3$ exist over $\mathbb{Q}$. We end with an application on the integral Brauer-Manin obstruction to the integral Hasse principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16042 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brauer groups of certain affine cubic surfaces Alfaraj, Abdulmuhsin Algebraic Geometry Number Theory 14F22, 14G12 We study the Brauer groups of affine surfaces that are complements of singular hyperplane sections of smooth cubic surfaces over a field $k$ of characteristic $0$. We determine the Brauer group over the algebraic closure as a Galois module for all the possible singular hyperplane sections. For the case when the hyperplane section is geometrically the union of three lines, we give explicit examples where transcendental elements of order $2$ and $3$ exist over $\mathbb{Q}$. We end with an application on the integral Brauer-Manin obstruction to the integral Hasse principle. |
| title | Brauer groups of certain affine cubic surfaces |
| topic | Algebraic Geometry Number Theory 14F22, 14G12 |
| url | https://arxiv.org/abs/2509.16042 |