论文标题
局部算术的用户指南
A user's guide to the local arithmetic of hyperelliptic curves
论文作者
论文摘要
最近已经开发了一种新的方法来研究过椭圆形曲线的算术$ y^2 = f（x）$，通过与$ f $的根相关的组合数据的奇数残留特征的本地字段。自引入以来，许多论文使用了这种“聚类图片”的机械来计算与这些曲线相关的众多算术不变的。本用户指南的目的是以独立的方式总结和集中所有这些结果，并以大量示例进行补充。
A new approach has been recently developed to study the arithmetic of hyperelliptic curves $y^2=f(x)$ over local fields of odd residue characteristic via combinatorial data associated to the roots of $f$. Since its introduction, numerous papers have used this machinery of "cluster pictures" to compute a plethora of arithmetic invariants associated to these curves. The purpose of this user's guide is to summarise and centralise all of these results in a self-contained fashion, complemented by an abundance of examples.
