椭圆曲线函数域的直纹剩余定理

A ruled residue theorem for function fields of conics

The ruled residue theorem characterises residue field extensions for valuations on a rational function field. Under the assumption that the characteristic of the residue field is different from $2$ this theorem is extended here to function fields of conics. The main result is that there is at most one extension of a valuation from on the base field to the function field of a conic for which the residue field extension is transcendental but not ruled. Furthermore the situation when this valuation is present is characterised.

超椭圆曲线函数域的规则留数定理

A ruled residue theorem for function fields of hyperelliptic curves

本文研究赋值到超椭圆曲线函数域的剩余超越扩张，证明了在特定剩余特征条件下，满足剩余域扩张超越但非规则的赋值扩展至多有限多个。

泛轨道留数与椭圆可求和性

Panorbital residues and elliptic summability

本文针对椭圆曲线平移自同构下的椭圆可求和性问题，引入两个新的泛轨道留数，证明其与已有轨道留数共同构成完全阻碍，并在复环面、Tate曲线和一维阿贝尔簇三种设定下建立理论、给出计算实例及若干独立新结果。