Motivic fundamental group and motivic Galois group

动机基本群和动机伽罗瓦群

• 批准号: 21740008
• 负责人: FURUSHO Hidekazu
• 金额: $ 2.83万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740008/
• 关键词: 数論幾何学; 基本群; 混合Tateモチーフ; 量子群; Grothendieck-Teichmuller群; 多重ゼータ値; KZ方程式; 混合Tateモティーフ; Grothendieck-Teichmull群

The Grothendieck-Teichmuller is the pro-algebraic group introduced by V. G. Drinfeld in 1990 as a deformation group of a certain type of quantum groups, which is defined by special three relations ; one pentagon equation and two hexagon equations. It is also worthy to note that in arithmetic geometry it is expected to coincide with the motivic Galois group of rational integers. I have found the unexpected fact that actually one pentagon equation implies the others, the two hexagon equations.Double shuffle relations and associators relations are two of the most known algebraic relations over rational numbers among multiple zeta values. Though actually both are conjectured to yield. the full set. of them, an interrelationship between these two relations was a mystery. P. Deligne and T. Terasoma posed a project(though incomplete) to deduce the former relations from the latter ones. One of my results is a final completion of their project. My method is quite different from theirs and actually it is based on really concise idea on K. T. Chen's bar construction calculus.

Grothendieck-Teichmuller群是由V. G. Drinfeld于1990年引入的一类由特殊三种关系定义的量子群的变形群；一个五边形方程和两个六边形方程。同样值得注意的是，在算术几何中，它被期望与有理数的动机伽罗瓦群相一致。我发现了一个意想不到的事实实际上一个五边形方程暗示了另外两个六边形方程。双重洗牌关系和结合子关系是有理数上多个zeta值之间最著名的两个代数关系。尽管实际上两者都被推测会让步。全套的。其中，这两种关系之间的相互关系是一个谜。P. Deligne和T. Terasoma提出了一个计划（虽然不完整），从后者推断出前者的关系。我的成果之一就是最终完成了他们的项目。我的方法和他们的很不一样，其实我的方法是基于陈冠希的酒吧构造演算的一个非常简洁的思想。

项目成果

Around associators

围绕关联者

• 发表时间: 2011
• 作者: K.Bannai;S.Kobayashi;T.Tsuji;S.Kobayashi;小林真一;小林真一;小林真一;小林真一;古庄英和;古庄英和;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho
• 通讯作者: Hidekazu Furusho

Geometric interpretation of double shuffle relation for multiple L-values

多个 L 值的双洗牌关系的几何解释

• 期刊: Proceedings of Kyoto 2010 "Galois-Teichmueller theory and Arithmetic Geometry"
• 作者: K.Bannai;S.Kobayashi;T.Tsuji;S.Kobayashi;小林真一;小林真一;小林真一;小林真一;古庄英和;古庄英和;Hidekazu Furusho;Hidekazu Furusho
• 通讯作者: Hidekazu Furusho

Various aspects of associators

关联者的各个方面

• 发表时间: 2011
• 作者: K.Bannai;S.Kobayashi;T.Tsuji;S.Kobayashi;小林真一;小林真一;小林真一;小林真一;古庄英和;古庄英和;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho
• 通讯作者: Hidekazu Furusho

Geometric interpretation of double shuffle relations of multiple polylogarithms at roots of unity

单位根处多个多对数的双洗牌关系的几何解释

• 发表时间: 2010
• 作者: K.Bannai;S.Kobayashi;T.Tsuji;S.Kobayashi;小林真一;小林真一;小林真一;小林真一;古庄英和;古庄英和;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho
• 通讯作者: Hidekazu Furusho

Motivic Hopf algebra and tree Hopf algebra (joint work with A.Jafari)

Motivic Hopf 代数和树 Hopf 代数（与 A.Jafari 合作）

• 发表时间: 2010
• 作者: K.Bannai;S.Kobayashi;T.Tsuji;S.Kobayashi;小林真一;小林真一;小林真一;小林真一;古庄英和;古庄英和;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho;Hidekazu Furusho
• 通讯作者: Hidekazu Furusho