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。这一代数几何中被广泛研究的问题已有近百年的历史。虽然它是完全解决的曲线在外地的特点0和有许多结果也在积极的特点，有到目前为止还没有一般的猜想，更不用说一般定理的曲线在外地的积极的特点。该项目将着眼于这一点和相关问题的某些例子类的代数曲线，以期找到一个一般的模式。

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.