通过普赖姆构造的 2∞ 塞尔默秩奇偶性

Pub Date : 2024-07-18 DOI:10.1016/j.jnt.2024.06.009
Jordan Docking
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引用次数: 0

摘要

我们推导出了一个 2 或 3 属曲线的雅各布秩的 2∞ 塞尔默秩奇偶性的局部公式。我们给出了一个明确的例子,说明这个局部公式如何给出秩奇偶性预测,从而可以检验2奇偶性猜想。我们的结果还应用于属 3 半稳曲线的奇偶性猜想。
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2∞-Selmer rank parities via the Prym construction

We derive a local formula for the parity of the 2-Selmer rank of Jacobians of curves of genus 2 or 3 which admit an unramified double cover. We give an explicit example to show how this local formula gives rank parity predictions against which the 2-parity conjecture may be tested. Our results yield applications to the parity conjecture for semistable curves of genus 3.

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