The Congruence Subgroup Problem and Groups of Finite Representation Type
The Congruence Subgroup Problem and Groups of Finite Representation Type
批准号:
9700474
负责人:
Andrei Rapinchuk
金额:
$4.99万
依托单位国家:
美国
项目类别:
Standard Grant
财政年份:
1997
资助国家:
美国
项目状态:
已结题
起止时间:
1997-07-01 至 2000-06-30
中文摘要
小行星9700474 该奖项提供资金,继续的同余子群问题的S-算术子群的线性代数群在数域。主要研究者将尝试使用各种技术,如不同的有界性条件(有界生成和类似性质),表示论的方法(Kazhdan的性质(T))等,来证明一些新类别的群的同余核的中心性,他还将研究具有有限表示类型的群的性质和一些有限生成群的表示变体。 本文的研究属于数论中的一般数学领域福尔斯。 数论有其历史根源,在研究整个数字,解决这样的问题,如那些处理整除一个整数由另一个。它是数学中最古老的分支之一,几个世纪以来,人们纯粹出于美学的原因而追求它。然而,在过去的半个世纪,它已成为一个不可或缺的工具,在不同的应用领域,如数据传输和处理,通信系统。
英文摘要
9700474 Rapinchuk This award provides funding for a continuing of the congruence subgroup problem for S-arithmetic subgroups of linear algebraic groups over number fields. The principal investigator will attempt to prove the centrality of the congruence kernel for some new classes of groups using a variety of techniques such as different boundedness conditions (bounded generation and similar properties), methods of representation theory (property (T) of Kazhdan), etc. He will also study the properties of groups having finite representation type and the representation varieties of some finitely generated groups. This research falls into the general mathematical field of Number Theory. Number Theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems.
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会议论文
Conference on Arithmetic Geometry and Algebraic Groups
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批准号:2305231
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项目类别:Standard Grant
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资助金额:$4.0万
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财政年份:2023
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负责人:Andrei Rapinchuk
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依托单位:
Elliptic Curves, Torsors, and L-functions
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批准号:1660462
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项目类别:Standard Grant
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资助金额:$1.5万
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财政年份:2017
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负责人:Andrei Rapinchuk
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依托单位:
Arithmetic and Zariski-dense subgroups in algebraic groups
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批准号:1301800
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项目类别:Standard Grant
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资助金额:$15.3万
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财政年份:2013
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负责人:Andrei Rapinchuk
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依托单位:
Arithmetic Groups, Their Applications and Generalizations
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批准号:0965758
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项目类别:Standard Grant
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资助金额:$15.32万
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财政年份:2010
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负责人:Andrei Rapinchuk
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依托单位:
SM: Arithmetic Groups and Their Applications in Combinatorics, Geometry and Topology
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批准号:1034750
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项目类别:Standard Grant
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资助金额:$1.0万
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财政年份:2010
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负责人:Andrei Rapinchuk
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依托单位:
Normal Subgroups of the Groups of Rational Points of Algebraic Groups, Congruence Subgroup Problem, and Related Topics
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批准号:0502120
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项目类别:Continuing Grant
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资助金额:$20.67万
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财政年份:2005
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负责人:Andrei Rapinchuk
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依托单位:
Normal Subgroup Structure of the Groups of Rational Points of Algebraic Groups and of Their Special Subgroups
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批准号:0138315
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项目类别:Continuing Grant
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资助金额:$12.4万
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财政年份:2002
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负责人:Andrei Rapinchuk
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依托单位:
The Congruence Subgroups Problem and Groups of Finite Representation Type
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批准号:9970148
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项目类别:Standard Grant
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资助金额:$7.2万
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财政年份:1999
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负责人:Andrei Rapinchuk
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依托单位:
国内基金
海外基金
山果蝇物种亚群(Drosophila montium species-subgroup)求偶行为及求偶歌进化及其相关基因研究
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批准号:31372187
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项目类别:面上项目
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资助金额:78.0万元
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批准年份:2013
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负责人:温硕洋
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依托单位: