Rational Points on Algebraic Varieties

代数簇上的有理点

• 批准号: 2371941
• 金额: --
• 依托单位: University of Bath
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2371941
• 关键词: Rational; Points; Algebraic; Varieties

My research centres on the distribution of rational points on algebraic varieties. In particular, I have proved and am aiming to prove results concerning the abundance and distribution of rational points on algebraic surfaces.Most of my research so far has focused on the Hilbert property, a geometric notion of the abundance of rational points on algebraic varieties with links to Zariski-density, weak weak approximation and the inverse Galois problem. My primary tool has been the theory of fibrations.During my first semester, I worked on proving the Hilbert property is satisfied for a certain class of double elliptic surfaces, namely diagonal quartic surfaces with certain coefficient conditions. Unfortunately, results which I hoped to prove were published during this time, but I gained a good deal of knowledge in the general theory of rational points and fibrations which I later applied in my research.

我的研究集中在代数簇上有理点的分布。特别是，我已经证明并且旨在证明有关代数曲面上有理点的丰度和分布的结果。到目前为止，我的大部分研究都集中在希尔伯特性质上，这是代数簇上有理点丰度的几何概念与 Zariski 密度、弱弱近似和逆伽罗瓦问题的联系。我的主要工具是纤维振动理论。在第一个学期，我致力于证明希尔伯特性质对于某类双椭圆曲面（即具有某些系数条件的对角四次曲面）是满足的。不幸的是，我希望证明的结果在这段时间发表了，但我获得了大量有理点和纤维一般理论的知识，后来我将这些知识应用到了我的研究中。