Genus zero modular operad and absolute Galois group

Combe, Noemie; Manin, Yuri I.

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学術論文

Genus zero modular operad and absolute Galois group

MPS-Authors

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Manin, Yuri I.
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://math.univ-lille1.fr/~nwejm/index.html
(出版社版)

https://doi.org/10.48550/arXiv.1907.10313
(プレプリント)

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Combe-Manin_Genus zero modular operad and absolute Galois group_2022.pdf
(出版社版), 304KB

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引用

Combe, N., & Manin, Y. I. (2022). Genus zero modular operad and absolute Galois group. North-Western European Journal of Mathematics, 8, 25-60.

引用: https://hdl.handle.net/21.11116/0000-000B-40DD-4

要旨

In this article, we develop the geometry of canonical stratifications of the
spaces $\mathcal{M}_{0,n}$ and prepare ground for studying the action of the
Galois group $Gal (\overline{\mathbb{Q}} /\mathbb{Q})$ upon strata. We define
and introduce a version of a gravity operad constructed for a class of moduli
spaces $\mathcal{M}_{0,n}$, equipped with a hidden holomorphic involution. This
additional symmetry is associated to a split quaternionic structure. We
introduce a categorical framework to present this object. Interaction between
the geometry, physics and the arithmetics are discussed. An important feature
is that 0-divisors of the split quaternion algebra imply additional singular
points, and lead to investigations concerning the geometry and mixed Hodge
structures.