Study of the structure of a tannakian category formed by equivalence classes of systems of linear inequalities over a number field

由数域上线性不等式组的等价类形成的坦纳基范畴的结构研究

• 批准号: 20540030
• 负责人: FUJIMORI Masami
• 金额: $ 1.5万
• 依托单位: Kanagawa Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540030/
• 关键词: 代数学; 数論; ディオファントス近似; 数体; 線型不等式; 淡中圏; 代数群; 表現

It is known that the equivalence classes of systems of linear inequalities which describe a rational approximation property of numbers are naturally identified with the representations of some group, but the whole body of the huge group is not clear yet.In this study, we have revealed via what algebraic group a classical system of linear inequalities which corresponds to the famous Roth inequality is considered a representation of the said huge group. We have also shown that arbitrary reductive groups appear in a natural manner as quotients of the above-mentioned huge group.

已知描述数的有理逼近性质的线性不等式组的等价类自然地等同于某个群的表示，但巨群的整体还不清楚，本文揭示了与著名的Roth不等式对应的经典线性不等式组通过什么代数群被认为是巨群的表示.我们还证明了任意约化群以一种自然的方式作为上述巨群的子群出现。

项目成果

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The algebraic groups leading to the Roth inequalities

导致罗斯不等式的代数群

• 发表时间: 2012
• 期刊: J. Theor. Nombres Bordeaux
• 作者: A.Bayad;浜畑芳紀;浜畑芳紀;浜畑芳紀;浜畑芳紀;藤森 雅巳
• 通讯作者: 藤森 雅巳

On algebraic groups attached to systems of linear inequalities over number fields

论依附于数域上线性不等式系统的代数群

• 发表时间: 2009
• 作者: A.Bayad;浜畑芳紀;浜畑芳紀;浜畑芳紀;浜畑芳紀;藤森 雅巳;藤森雅巳;藤森雅巳
• 通讯作者: 藤森雅巳