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Mathematical Sciences: Semi-simple Groups and Arithmetic Subgroups

Mathematical Sciences: Semi-simple Groups and Arithmetic Subgroups
数学科学:半单群和算术子群
批准号:
9204296
负责人:
Gopal Prasad
金额:
$9.0万
依托单位国家:
美国
项目类别:
Continuing Grant
财政年份:
1992
资助国家:
美国
项目状态:
已结题
起止时间:
1992-06-15 至 1995-11-30

项目摘要

项目成果

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中文摘要
翻译
Prasad教授将研究与局部和全局半单群相关的算术、几何和群论问题。他打算研究全局函数域上各向异性半简单群的同余子群问题。他还打算研究某些光滑品种的主束。这个项目属于算术几何的一般领域,它融合了数学中两个最古老的领域:数论和几何。事实证明,这一组合非常富有成效——最近解决了几代人经受住了考验的问题。其诸多后果之一是新的纠错码。这些代码对现代计算机(硬盘)和光盘都是必不可少的。
英文摘要
Professor Prasad will work on arithmetic, geometric and group theoretic questions related to semi-simple groups over local and global fields. He intends to work on the congruence subgroup problem for anisotropic semi-simple groups over global function fields. He also intends to study principal bundles over certain smooth varieties. This project falls into the general area of arithmetic geometry - a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.
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会议论文
Algebraic groups, arithmetic subgroups and geometry
Algebraic Groups, Arithmetic Groups and Locally Symmetric Spaces
Arithmetic, Geometry and Representation Theory of Reductive Groups
Arithmetic and Representation Theory of Reductive Groups over Local and Global Fields
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