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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.16372 |
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| _version_ | 1866916975524970496 |
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| author | Navone, Giorgio |
| author_facet | Navone, Giorgio |
| contents | Given a cubic curve $C$ over a number field, we consider the K3 surface $Y_C$ constructed as the minimal desingularisation of the quotient of $C \times C$ by an automorphism of order 3. We relate the transcendental Brauer groups of $Y_C$ and $C \times C$, allowing us to explicitly compute the former group in the case of a diagonal cubic curve defined over $\mathbb{Q}$. We obtain conjectural insight on the existence of Galois cubic points over $\mathbb{Q}$ for everywhere locally soluble diagonal cubic curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16372 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transcendental Brauer groups of cubic generalised Kummer surfaces Navone, Giorgio Number Theory Algebraic Geometry Given a cubic curve $C$ over a number field, we consider the K3 surface $Y_C$ constructed as the minimal desingularisation of the quotient of $C \times C$ by an automorphism of order 3. We relate the transcendental Brauer groups of $Y_C$ and $C \times C$, allowing us to explicitly compute the former group in the case of a diagonal cubic curve defined over $\mathbb{Q}$. We obtain conjectural insight on the existence of Galois cubic points over $\mathbb{Q}$ for everywhere locally soluble diagonal cubic curves. |
| title | Transcendental Brauer groups of cubic generalised Kummer surfaces |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2506.16372 |