Galois module theory for curves over finite fields

这个项目是关于确定代数曲线上的整体全纯微分空间的等变结构。这个在代数几何中被广泛研究的问题已经有大约100年的历史了。特征为0的域上的曲线已完全解决，正特征线也有许多结果，但至今还没有一般的猜想，更不用说正特征域上的曲线的一般定理了。该项目将着眼于某些代数曲线的实例类的这一问题和相关问题，以期找到一个普遍的模式。

The project is about determining the equivariant structure of the space of global holomorphic differentials on an algebraic curve. This widely studied problem in Algebraic Geometry has a history of about 100 years. While it is completely solved for curves over fields of characteristic 0 and there are many results also in positive characteristic, there is so far no general conjecture, let alone general theorem for curves over fields of positive characteristic. The project will look at this and related problems for certain example classes of algebraic curves with a view towards finding a general pattern.