What is the action of $mathrmGal(overlinemathbbQ/mathbbQ)$ on the Teichmuller tower?

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The basis of Grothendieck's esquisse d'un programme is that there exists an action of the absolute galois group of the rationals on the Teichmuller tower, the collection of all etale fundamental groups of the moduli spaces of algebraic curves. Not only this, but apparently Belyi's theorem can be used to prove that it is already faithful on $pi_1^et(mathcalM_0,4)$.



I've looked at quite a few resources discussing this and none of them actually explicitly define what this action is (or what it is induced by). Are there any resources that explicitly define the action and give a proof using Belyi's theorem that this action is faithful?



Thanks for any help.




algebraic-geometry galois-theory




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  • This paper seems to give lots of references: ncatlab.org/nlab/files/StiXGaloisAndGT.pdf
    – Henrique Augusto Souza
    Jul 31 at 1:43















up vote
3
down vote

favorite












The basis of Grothendieck's esquisse d'un programme is that there exists an action of the absolute galois group of the rationals on the Teichmuller tower, the collection of all etale fundamental groups of the moduli spaces of algebraic curves. Not only this, but apparently Belyi's theorem can be used to prove that it is already faithful on $pi_1^et(mathcalM_0,4)$.



I've looked at quite a few resources discussing this and none of them actually explicitly define what this action is (or what it is induced by). Are there any resources that explicitly define the action and give a proof using Belyi's theorem that this action is faithful?



Thanks for any help.




algebraic-geometry galois-theory




share|cite|improve this question



















  • This paper seems to give lots of references: ncatlab.org/nlab/files/StiXGaloisAndGT.pdf
    – Henrique Augusto Souza
    Jul 31 at 1:43













up vote
3
down vote

favorite









up vote
3
down vote

favorite











The basis of Grothendieck's esquisse d'un programme is that there exists an action of the absolute galois group of the rationals on the Teichmuller tower, the collection of all etale fundamental groups of the moduli spaces of algebraic curves. Not only this, but apparently Belyi's theorem can be used to prove that it is already faithful on $pi_1^et(mathcalM_0,4)$.



I've looked at quite a few resources discussing this and none of them actually explicitly define what this action is (or what it is induced by). Are there any resources that explicitly define the action and give a proof using Belyi's theorem that this action is faithful?



Thanks for any help.




algebraic-geometry galois-theory




share|cite|improve this question











The basis of Grothendieck's esquisse d'un programme is that there exists an action of the absolute galois group of the rationals on the Teichmuller tower, the collection of all etale fundamental groups of the moduli spaces of algebraic curves. Not only this, but apparently Belyi's theorem can be used to prove that it is already faithful on $pi_1^et(mathcalM_0,4)$.



I've looked at quite a few resources discussing this and none of them actually explicitly define what this action is (or what it is induced by). Are there any resources that explicitly define the action and give a proof using Belyi's theorem that this action is faithful?



Thanks for any help.





algebraic-geometry galois-theory





share|cite|improve this question










share|cite|improve this question




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asked Jul 31 at 0:10









Tsein32

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  • This paper seems to give lots of references: ncatlab.org/nlab/files/StiXGaloisAndGT.pdf
    – Henrique Augusto Souza
    Jul 31 at 1:43

















  • This paper seems to give lots of references: ncatlab.org/nlab/files/StiXGaloisAndGT.pdf
    – Henrique Augusto Souza
    Jul 31 at 1:43
















This paper seems to give lots of references: ncatlab.org/nlab/files/StiXGaloisAndGT.pdf
– Henrique Augusto Souza
Jul 31 at 1:43





This paper seems to give lots of references: ncatlab.org/nlab/files/StiXGaloisAndGT.pdf
– Henrique Augusto Souza
Jul 31 at 1:43
















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