Mathematical Sciences: Arithmetic of Abelian Varieties

数学科学：阿贝尔簇算术

• 批准号: 8700790
• 负责人: Alice Silverberg
• 金额: $ 2.92万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8700790&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Arithmetic; Abelian; Varieties

This research concentrates on questions in number theory and arithmetical algebraic geometry related to abelian varieties. Topics for research include the determination of "Mordell-Weil groups" of generic abelian varieties, bounding orders of torsion points on abelian varieties defined over number fields, and the development of criteria for when an abelian variety has a model rational over its field of moduli. In arithmetical algebraic geometry one interprets the equations in number as a geometric object. If the equations are nice enough this geometric object has a way of combining points to get new points (i.e. combining solutions to get new solutions). When this happens one has what is called an abelian variety. These types of equations are very important and contain huge amounts of structure. The P.I. will spend her time during this research studying this situation. Even though she is a relatively new PhD she already has some excellent results to her credit. This research will undoubtedly result in many more.

这项研究集中在数论问题， 与交换簇有关的算术代数几何学。 研究课题包括确定“莫德尔-韦伊 群”的一般阿贝尔簇，挠的界序 定义在数域上的阿贝尔簇上的点， 发展当阿贝尔变种有一个模型时的标准 模域上的有理数 在算术代数几何中， 数的方程作为几何对象。 如果方程是 这个几何物体有一种很好的方法， 以获得新的点（即，组合解决方案以获得新的 解决方案）。 当这种情况发生时，就有了所谓的阿贝尔群 品种 这些类型的方程非常重要，包含 大量的结构。 私家侦探会花时间 这项研究研究了这种情况。 即使她是一个 相对较新的博士，她已经有一些优秀的结果，她 信用 这项研究无疑会带来更多的成果。