Refined obstructions to local-global principles for 0-cycles
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918492494626816 |
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| author | Balestrieri, Francesca Greven, Anouk Newton, Rachel Sankar, Soumya Santicola, Katerina Trip, Manoy |
| author_facet | Balestrieri, Francesca Greven, Anouk Newton, Rachel Sankar, Soumya Santicola, Katerina Trip, Manoy |
| contents | We introduce new `refined' obstructions to local-global principles for 0-cycles on algebraic varieties over number fields. Assuming finiteness of relevant Tate--Shafarevich groups, we show that the Hasse principle and weak approximation for 0-cycles on generalised Kummer varieties and bielliptic surfaces are controlled by obstructions of this new type. As an additional application of our refined obstructions, we answer a question of Zhang about the relationship between the Brauer--Manin and connected descent obstructions for 0-cycles. We also show that a Corwin--Schlank style refined obstruction set coincides with the set of global 0-cycles, conditionally on the Section Conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08972 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Refined obstructions to local-global principles for 0-cycles Balestrieri, Francesca Greven, Anouk Newton, Rachel Sankar, Soumya Santicola, Katerina Trip, Manoy Algebraic Geometry Number Theory 14G12 (Primary), 11G35, 14G05, 14C25, 14K15, 11G10 (Secondary) We introduce new `refined' obstructions to local-global principles for 0-cycles on algebraic varieties over number fields. Assuming finiteness of relevant Tate--Shafarevich groups, we show that the Hasse principle and weak approximation for 0-cycles on generalised Kummer varieties and bielliptic surfaces are controlled by obstructions of this new type. As an additional application of our refined obstructions, we answer a question of Zhang about the relationship between the Brauer--Manin and connected descent obstructions for 0-cycles. We also show that a Corwin--Schlank style refined obstruction set coincides with the set of global 0-cycles, conditionally on the Section Conjecture. |
| title | Refined obstructions to local-global principles for 0-cycles |
| topic | Algebraic Geometry Number Theory 14G12 (Primary), 11G35, 14G05, 14C25, 14K15, 11G10 (Secondary) |
| url | https://arxiv.org/abs/2605.08972 |