We generalize the explicit quadratic Chabauty techniques for integral points on odd degree hyperelliptic curves and for rational points on genus 2 bielliptic curves to arbitrary number fields using restriction of scalars. This is achieved by combining equations coming from Siksek’s extension of classical Chabauty with equations defined in terms of p-adic heights attached to independent continuous idele class characters. We give several examples to show the practicality of our methods.

中文翻译：

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数字字段上的显式二次 Chabauty

我们使用标量限制将用于奇次超椭圆曲线上的积分点和属 2 双椭圆曲线上的有理点的显式二次 Chabauty 技术推广到任意数域。这是通过将来自 Siksek 对经典 Chabauty 的扩展的方程与根据p- adic 高度定义的方程相结合来实现的，这些方程附加到独立的连续理想类字符。我们举了几个例子来展示我们方法的实用性。