Mathematical Sciences: Higher Regulators, Algebraic Cycles, and Values of L-functions

数学科学：高级调节器、代数循环和 L 函数的值

• 批准号: 8703602
• 负责人: Dinakar Ramakrishnan
• 金额: --
• 依托单位: Cornell University
• 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: 1987-07-01 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8703602&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Higher; Regulators; Algebraic

This research will continue the investigations of the P.I. on the structure of cycles and K-theory of arithmetic varieties and their (conjectural) relationship to values of L-functions at integral points. He will analyze certain selected conjectures of Beilinson, Bloch and Tate in the context of modular varieties where one can use the theory of automorphic forms. This research is in the blend of topics encompassing number theory, algebraic geometry and automorphic forms. That is, it brings to bear tools from algebra, analysis and geometry to analyze number theoretic problems. The "values of L-functions" give analytic expression to explicit numbers of great arithmetic significance allowing for their deeper study. The P.I. has contributed many interests results to this area in the past and will surely do so further during this research.

这项研究将继续P.I.的调查。 圈的结构与算术簇的K-理论 以及它们与L-函数值的关系， 积分点 他将分析某些精选的 模块变体语境中的贝林森、布洛赫和泰特 可以用自守形式理论 本研究是一个多学科交叉的研究， 理论，代数几何和自守形式。 即它 运用代数、分析和几何等工具， 分析数论问题。 “L-函数的值” 给出大算术中显式数的解析表达式 其重要性，使其更深入的研究。 私家侦探具有 过去在这一领域贡献了许多利益成果， 在这次研究中，我们一定会继续这样做。