Descent of algebraic curves

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The project considers the fields of definition of a given algebraic curve. The concrete question is, whether one can decide effectively, whether such a curve can be defined by simple equations. One then says that the curve descends. In this can the calculations on these curves and the description of their arithmetic properties are more accessible.The research project aims to develop algorithmic criteria that decide whether a given curve descends or not, and to descend the curve explicitly if possible. The implementation of these algorithms and their open accessibility are an essential part of the project.