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

Alexander Petrov

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

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arxiv 2109.09301 v3 pith:CRVBSYPK submitted 2021-09-20 math.NT math.AG

Alexander Petrov This is my paper · ORCID

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keywords groupfundamentalgaloisactionappearscomingcompletionfield

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abstract

We prove that any semi-simple 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 $3$ punctures.

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The motivic fundamental groupoid at tangential basepoints
math.AG 2025-10 conditional novelty 8.0 of 10

A general motivic fundamental groupoid at tangential basepoints is constructed over any field, with Betti and de Rham realizations matching the classical fundamental torsor and periods given by regularized iterated integrals.

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