Descent of algebraic curves

该项目考虑了给定代数曲线的定义域。具体的问题是，一个人能否有效地决定，这样一条曲线是否可以用简单的方程来定义。然后有人说，曲线是下降的。在这种情况下，这些曲线的计算和它们的算术性质的描述更容易。研究项目的目的是开发算法准则来确定给定的曲线是否下降，并在可能的情况下明确地下降曲线。这些算法的实现及其开放的可访问性是该项目的重要组成部分。

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.