Computational Algebraic approach to anabelian geometry

2014 Fiscal Year Final Research Report

• Project/Area Number: 24654006
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Osaka University (2013-2014); Okayama University (2012)
• Principal Investigator: NAKAMURA Hiroaki 大阪大学, 理学(系)研究科(研究院), 教授 (60217883)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 遠アーベル幾何 / 曲面写像類群 / グロタンディークデッサン / 楕円曲線 / 分岐被覆

Outline of Final Research Achievements

We studied computational aspects of irreducible decomposition of graded modules arising from weight filtrations of mapping class groups of surfaces. In particular, we obtained results that fix certain parts of the stable image of the Johnson homomorphism in the case of genus zero. We also advanced a computational algebraic approach to X-shape, Y-shaped plane trees defined over the rational number field, and found several remarkable series of Pakovich-Zapponi type examples of Grothendieck dessins of genus one associated with them.

Free Research Field

代数学