On binary quartics and the Cassels-Tate pairing (Q2081522)
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scientific article; zbMATH DE number 7600666
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On binary quartics and the Cassels-Tate pairing |
scientific article; zbMATH DE number 7600666 |
Statements
On binary quartics and the Cassels-Tate pairing (English)
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13 October 2022
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In this paper a new formula for the Cassels-Tate pairing on the \(2\)-Selmer group of an elliptic curve is given. Different from previous methods, this formula does not require to solve any conics. The construction relies on extensive study of a certain \(K3\)-surface defined as a complete intersection of three forms of degree 2.
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Cassels-Tate pairing
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Tate-Shafarevich groups
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elliptic curves
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