Universality of the Galois action on the fundamental group of $\mathbb{P}^{1}\setminus\{0,1,\infty\}$

Alexander Petrov

doi:10.4171/jems/1631

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Universality of the Galois action on the fundamental group of $P^{1} ∖ {0, 1, \infty}$

Alexander Petrov
Institute for Advanced Study, Princeton, USA

$Universality of the Galois action on the fundamental group of $\mathbb{P}^{1}\setminus\{0,1,\infty\}$ cover$

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Abstract

We prove that any semisimple representation of the Galois group of a number field coming from geometry appears as a subquotient of the ring of regular functions on the pro-algebraic completion of the fundamental group of the projective line with three punctures.

Cite this article

Alexander Petrov, Universality of the Galois action on the fundamental group of $P^{1} ∖ {0, 1, \infty}$ . J. Eur. Math. Soc. (2025), published online first

DOI 10.4171/JEMS/1631