Corpus ID: 237571790

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

@inproceedings{Petrov2021UniversalityOT,
title={Universality of the Galois action on the fundamental group of \$\mathbb\{P\}^1\setminus\\{0,1,\infty\\}\$},
author={Alexander Petrov},
year={2021}
}
• Alexander Petrov
• Published 20 September 2021
• Mathematics
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.

#### References

SHOWING 1-10 OF 30 REFERENCES
On Galois Extensions of a Maximal Cyclotomic Field
This paper is devoted to the realization of certain types of Chevalley groups as the Galois group of extensions of certain cyclotomic fields. In addition, a criterion for an algebraic curve to beExpand
Geometrically irreducible $p$-adic local systems are de Rham up to a twist
We prove that any geometrically irreducible Qp-local system on a smooth algebraic variety over a p-adic field K becomes de Rham after a twist by a character of the Galois group of K. In particular,Expand
On ℓ-adic Pro-algebraic and Relative Pro-ℓ Fundamental Groups
We recall l-adic relative Malcev completions and relative pro-l completions of pro-finite groups and homotopy types. These arise when studying unipotent completions of fibres or of normal subgroups.Expand
The Proalgebraic Completion of Rigid Groups
• Mathematics
• 2002
A finitely generated group Γ is called representation rigid (briefly, rigid) if for every n, Γ has only finitely many classes of simple ℂ representations in dimension n. Examples include higher rankExpand
The arithmetic of fundamental groups : PIA 2010
• Mathematics
• 2012
Part I Heidelberg Lecture Notes: 1 Heidelberg lectures on Coleman integration by A.Besser.- 2 Heidelberg lectures on fundamental groups by T. Szamuely.- Part II The Arithmetic of Fundamental Groups:Expand
Lectures on K3 Surfaces
Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular and each chapter ends with questions and open problems. Expand
Lefschetz theorems for tamely ramified coverings
• Mathematics
• 2015
As is well known, the Lefschetz theorems for the \'etale fundamental group of SGA1 do not hold. We fill a small gap in the literature showing they do for tame coverings. Let $X$ be a regularExpand
Modular Forms
Modular Forms and Dirichlet SeriesBy Andrew Ogg. (Mathematics Lecture Notes Series.) Pp. xviii + 173. (W. A. Benjamin: New York and Amsterdam, 1969.) n.p.
Le Groupe Fondamental de la Droite Projective Moins Trois Points
Le present article doit beaucoup a A. Grothendieck. Il a invente la philosophie des motifs, qui est notre fil directeur. Il y a quelques cinq ans, il m’a aussi dit, avec force, que le completeExpand
Chtoucas de Drinfeld et correspondance de Langlands
Résumé.On démontre la correspondance de Langlands pour GLr sur les corps de fonctions. La preuve généralise celle de Drinfeld en rang 2 : elle consiste à réaliser la correspondance en rang r dans laExpand