Mathematical Sciences: Complex Multiplication of Higher-Dimensional Drinfeld Modules

数学科学：高维德林菲尔德模的复数乘法

• 批准号: 8902621
• 负责人: Greg Anderson
• 金额: $ 8.46万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-15 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902621&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Complex; Multiplication; Higher

The Principal Investigator's project is to develop a reciprocity law governing the behavior of torsion points on higher-dimensional analogues of Drinfeld modules; he calls these Abelian A-modules. One of the products of this would be to attach a Hecke character to each Abelian A-module with complex multiplication, and develop the theory of L-series attached to such characters, following the work of Goss. This research is work in the Algebraic Geometry of finite characteristic. Although the field originated with notions of continuously varying geometric structures like lines and planes, in this context the Discrete takes over, and methods akin to those from the theory of whole numbers are most useful. Reciprocally, the algebraic geometry of finite characteristic is now having great influence on the Theory of Numbers, and is finding application in Computer Science and Coding Theory.

首席研究员的项目是开发一个 上扭点行为的互反律 更高维类似的德林费尔德模块;他呼吁 这些阿贝尔A模其中一个产品就是 给每个阿贝尔A-模加上一个Hecke特征标， 复数乘法，发展了L-级数理论 附在这样的字符，下面的工作戈斯。 本研究是在有限代数几何中进行的 特色虽然这个领域起源于 连续变化的几何结构，如线条， 平面，在这种情况下，离散接管，方法 类似于整数理论的那些是最有用的。 反过来，有限特征的代数几何 现在对数论有很大的影响， 在计算机科学和编码理论中找到应用。