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We prove that any semi-simple representation of the Galois group of a numberfield coming from geometry appears as a subquotient of the ring of regularfunctions on the pro-algebraic completion of the fundamental group of theprojective line with $3$ punctures.

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