Galois module theory for curves over finite fields

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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.