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arXiv · 2109.08258

Computing the Cassels-Tate Pairing for Genus Two Jacobians with Rational Two Torsion Points

Jiali Yan
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Abstract

In this paper, we give an explicit formula as well as a practical algorithm for computing the Cassels-Tate pairing on $\text{Sel}^{2}(J) \times \text{Sel}^{2}(J)$ where $J$ is the Jacobian variety of a genus two curve under the assumption that all points in $J[2]$ are $K$-rational. We also give an explicit formula for the Obstruction map $\text{Ob}: H^1(G_K, J[2]) \rightarrow \text{Br}(K)$ under the same assumption. Finally, we include a worked example demonstrating we can indeed improve the rank bound given by a 2-descent via computing the Cassels-Tate pairing.

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Jiali Yan. 2021-09-17. Computing the Cassels-Tate Pairing for Genus Two Jacobians with Rational Two Torsion Points. https://arxiv.org/abs/2109.08258

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