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Teichmueller curves, Galois actions and GT-relations

Martin Moeller
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Abstract

Teichmueller curves are geodesic discs in Teichmueller space that project to algebraic curves $C$ in the moduli space $M_g$. Some Teichmüller curves can be considered as components of Hurwitz spaces. We show that the absolute Galois group $G_\QQ$ acts faithfully on the set of these embedded curves. We also compare the action of $G_\QQ$ on $π_1(C)$ with the one on $π_1(M_g)$ and obtain a relation in the Grothendieck-Teichmueller group, seemingly independent of the known ones.

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Martin Moeller. 2004-10-11. Teichmueller curves, Galois actions and GT-relations. https://arxiv.org/abs/math/0311308

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