Descent of algebraic curves

代数曲线下降

• 批准号: 438058067
• 负责人: Professor Dr. Jeroen Sijsling
• 金额: --
• 依托单位: Institut für Reine Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2020
• 资助国家: 德国
• 起止时间: 2019-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/438058067?language=en
• 关键词: Descent; algebraic; curves

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.

该项目认为领域的定义一个给定的代数曲线。具体的问题是，人们是否能够有效地决定，这样的曲线是否能够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，对这些曲线的计算和对它们的算术属性的描述更加容易理解。该研究项目旨在开发算法标准，以确定给定曲线是否下降，并在可能的情况下显式地下降曲线。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。