Mathematical Sciences: Presidential Young Investigator

数学科学：总统青年研究员

• 批准号: 8857208
• 负责人: Karl Rubin
• 金额: $ 19.95万
• 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: 1988
• 资助国家: 美国
• 起止时间: 1988-08-01 至 1994-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8857208&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Presidential; Young; Investigator

This research is primarily concerned with arithmetic on elliptic curves with complex multiplication, especially questions related to the Birch and Swinnerton-Dyer conjecture, Iwasawa theory and p-adic L-functions. Three specific problems are mentioned. The first is to show that the invariant Sha is finite and to give evidence for its conjectured order. The second is to study the p-adic analogues of the Birch and Swinnerton-Dyer conjecture. The third is to determine certain special units in abelian extensions of fields of complex multiplication since these would very likely enable one to extend the earlier results to higher dimensional abelian varieties with complex multiplication.

这项研究主要涉及算术上 具有复数乘法的椭圆曲线，特别是问题 关于Birch和Swinnerton-Dyer猜想，Iwasawa 理论和p进L函数。 三个具体问题是 人所提及 第一个是证明不变量Sha是有限的 并为它的命令提供证据。 二是 研究Birch和Swinnerton-Dyer的p-adic类似物 猜想 第三是确定某些特殊单位， 复乘法域的交换扩张，因为 这很可能使人们能够推广早期的结果 到高维阿贝尔簇， 乘法