论文标题
模块化的Dessins和Grothendieck-Teichmuller集团
Dessins for Modular Operad and Grothendieck-Teichmuller Group
论文作者
论文摘要
Grothendieck研究Galois组$ g _ {\ Mathbb Q} $的一部分$π_1（{\ Mathbb p}^1 \ setMinus \ {0,1，\ infty \}）$的profinite完成。后者通过有限的图表“ Dessins d'Enfant”接受了一个很好的组合编码。在过去的几十年中，这部分是从A. Belyi，V。Drinfeld和Y. Ihara的基础作品开始的。我们的简要说明涉及Grothendieck程序的另一部分，其中其几何环境扩展到代数曲线的模量空间，更具体地说，是零属稳定曲线，具有标记/标记的点。我们的主要目标是证明此类曲线的双图可能在适当的操作环境中扮演“模块化Dessins”的角色。
A part of Grothendieck's program for studying the Galois group $G_{\mathbb Q}$ of the field of all algebraic numbers $\overline{\mathbb Q}$ emerged from his insight that one should lift its action upon $\overline{\mathbb Q}$ to the action of $G_{\mathbb Q}$ upon the (appropriately defined) profinite completion of $π_1({\mathbb P}^1 \setminus \{0,1, \infty\})$. The latter admits a good combinatorial encoding via finite graphs "dessins d'enfant". This part was actively developing during the last decades, starting with foundational works of A. Belyi, V. Drinfeld and Y. Ihara. Our brief note concerns another part of Grothendieck program, in which its geometric environment is extended to moduli spaces of algebraic curves, more specifically, stable curves of genus zero with marked/labelled points. Our main goal is to show that dual graphs of such curves may play the role of "modular dessins" in an appropriate operadic context.
