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Mathematical Sciences: Presidential Young Investigator

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
依托单位国家:
美国
项目类别:
Continuing Grant
财政年份:
1988
资助国家:
美国
项目状态:
已结题
起止时间:
1988-08-01 至 1994-01-31

项目摘要

项目成果

Karl Rubin的其他基金

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相关文献

中文摘要
翻译
本文主要研究了椭圆曲线的复乘法运算,特别是与Birch和Swinnerton-Dyer猜想、Iwasawa理论和p进l函数有关的问题。文中提到了三个具体问题。第一个是证明不变量Sha是有限的,并为它的猜想次序提供证据。第二步是研究Birch猜想和Swinnerton-Dyer猜想的p进类比。第三个是确定复乘法域的阿贝尔扩展中的某些特殊单位,因为这些很可能使人们能够将先前的结果扩展到具有复乘法的高维阿贝尔变体。
英文摘要
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.
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FRG: Collaborative Research: Definability and Computability over Arithmetically Significant Fields
  • 批准号:
    2152262
  • 项目类别:
    Standard Grant
  • 资助金额:
    $17.11万
  • 财政年份:
    2022
  • 负责人:
    Karl Rubin
  • 依托单位:
Selmer Groups, Euler Systems, and Rational Points on Curves
  • 批准号:
    1500316
  • 项目类别:
    Standard Grant
  • 资助金额:
    $17.0万
  • 财政年份:
    2015
  • 负责人:
    Karl Rubin
  • 依托单位:
Variation of Selmer groups
  • 批准号:
    1065904
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $31.28万
  • 财政年份:
    2011
  • 负责人:
    Karl Rubin
  • 依托单位:
Arithmetic of elliptic curves and abelian varieties
  • 批准号:
    0757807
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $17.0万
  • 财政年份:
    2008
  • 负责人:
    Karl Rubin
  • 依托单位:
国内基金
海外基金
Handbook of the Mathematics of the Arts and Sciences的中文翻译
  • 批准号:
    12226504
  • 项目类别:
    数学天元基金项目
  • 资助金额:
    20.0万元
  • 批准年份:
    2022
  • 负责人:
    黄朝凌
  • 依托单位:
SCIENCE CHINA: Earth Sciences
Journal of Environmental Sciences
SCIENCE CHINA Information Sciences