On genus one curves violating the local-global principle (Q2079484)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On genus one curves violating the local-global principle |
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On genus one curves violating the local-global principle (English)
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30 September 2022
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Let \(K\) be a number field which is not containing \(\mathbb{Q}(i)\). In this constructive paper that is under review, the author finds an elliptic curve \(E\) defined over \(K\) such that its Shafarevich-Tate group has a nontrivial \(2\)-torsion subgroup. This is exactly a positive answer to Clark's conjecture.
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rational points
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local-global principle
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genus one curves
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Brauer-Manin obstruction
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