Motivic fundamental group and motivic Galois group
Project/Area Number |
21740008
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Single-year Grants |
Research Field |
Algebra
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Research Institution | Nagoya University |
Principal Investigator |
FURUSHO Hidekazu 名古屋大学, 多元数理科学研究科, 准教授 (60377976)
|
Project Period (FY) |
2009 – 2011
|
Project Status |
Completed (Fiscal Year 2011)
|
Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
Keywords | 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 |
Research Abstract |
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.
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Report
(4 results)
Research Products
(44 results)
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[Presentation]2012
Organizer
Low dimensional topology and number theory IV
Place of Presentation
Kyushu University, Fukuoka, JAPAN
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[Presentation]2012
Organizer
5th Multiple Zeta Values seminar
Place of Presentation
Kyushu University, Hakata, Japan
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[Presentation]2011
Organizer
Auto orphic forms and Galois representations
Place of Presentation
Durham University, Durham, UK
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[Presentation]2011
Organizer
Low dimensional topology and number theoryIII
Place of Presentation
Nishijin Plaza, Fukuoka, JAPAN
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[Presentation]2009
Organizer
p-adic Special Functions and Arithmetic Geometry
Place of Presentation
Yutomorikurabu, Zaoh, Japan
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[Presentation]2009
Organizer
54th Algebra Symposium
Place of Presentation
University, Tokyo, Japan
Related Report