Mathematical Sciences: Cohomology of Arithmetic Groups

数学科学：算术群的上同调

• 批准号: 8701758
• 负责人: Avner Ash
• 金额: --
• 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 1990-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701758&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Cohomology; Arithmetic; Groups

This research will be in the cohomology of arithmetic groups and the related automorphic forms. It will concentrate on three areas. The first is the generalized modular symbols and the ghost classes. They will be studied via the representation theory of certain finite groups. The second is the congruences between cohomology classes with different coefficient modules and between the associated eigenvalues of the Hecke algebra. This leads to construction of torsion cohomology from cusp forms. There is a conjectural link with large representations of the Galois group of the rational numbers. The third area is a computer-aided calculation of cohomology groups. This research contains an interesting blend of algebra and analysis which is used to study questions in number theory. This is an important and very deep study which the P.I. has been very successful at in the past. He will undoubtedly continue to produce striking results during the tenure of this award.

这项研究将是算术群的上同调和相关的自同构形式。 它将集中在三个领域。 第一个是广义模块化符号和幽灵类。 它们将通过某些有限群的表示论来研究。 第二个是具有不同系数模的上同调类之间以及赫克代数的相关特征值之间的同余。 这导致从尖点形式构造扭转上同调。 与有理数伽罗瓦群的大型表示存在猜想的联系。 第三个领域是上同调群的计算机辅助计算。 这项研究有趣地融合了代数和分析，用于研究数论中的问题。 这是一项重要且非常深入的研究，P.I.过去一直非常成功。 毫无疑问，他将在该奖项任职期间继续创造惊人的成果。