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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.02115 |
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| _version_ | 1866913635039707136 |
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| author | Izquierdo, Diego Liang, Yongqi Zhang, Hui |
| author_facet | Izquierdo, Diego Liang, Yongqi Zhang, Hui |
| contents | It is conjectured that the Brauer--Manin obstruction is expected to control the existence of 0-cycles of degree 1 on smooth proper varieties over number fields. In this paper, we prove that the existence of Brauer--Manin obstruction to Hasse principle for 0-cycles of degree 1 on the product of smooth (non-necessarily proper) varieties is equivalent to the simultaneous existence of such an obstruction on each factor. We also prove an analogous statement for smooth varieties defined over function fields of $\mathbb{C}((t))$-curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02115 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Product of Brauer--Manin obstruction for 0-cycles over number fields and function fields Izquierdo, Diego Liang, Yongqi Zhang, Hui Algebraic Geometry It is conjectured that the Brauer--Manin obstruction is expected to control the existence of 0-cycles of degree 1 on smooth proper varieties over number fields. In this paper, we prove that the existence of Brauer--Manin obstruction to Hasse principle for 0-cycles of degree 1 on the product of smooth (non-necessarily proper) varieties is equivalent to the simultaneous existence of such an obstruction on each factor. We also prove an analogous statement for smooth varieties defined over function fields of $\mathbb{C}((t))$-curves. |
| title | Product of Brauer--Manin obstruction for 0-cycles over number fields and function fields |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2501.02115 |