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I would like to understand Grothendieck's Esquisse d'un Programme more. Are there any references that would help me, and are there modern works pursuing the same themes?

At this point I am still currently learning algebraic geometry, but I am familiar with the idea of moduli spaces as parametrizing families of curves (or more general objects) as well as the fundamental group from algebraic topology. I would like to know more as to what I should study next if I am interested in the ideas presented in the Esquisse d'un Programme.

Anton Hilado
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    Look here: http://www.cambridge.org/us/academic/subjects/mathematics/number-theory/geometric-galois-actions-volume-1 – KConrad Feb 05 '16 at 04:22
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    As Esquisse has several distinct threads it would help if you gave more precision on what parts you want to concentrate on. – Tim Porter Feb 05 '16 at 11:26
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    I think that this MO question about Grothendieck's Dessins d'Enfants could be of interest to you:

    http://mathoverflow.net/questions/1909/what-are-dessins-denfants You may begin with this part of his Esquisse.

     – Pedro Montero Feb 05 '16 at 12:01
  • Thanks for all your responses! If I had to be specific I guess I find the second and third sections to be the most interesting, which I believe concerns moduli and Teichmuller spaces, the projective line with three points removed, and the already mentioned Dessins d'Enfants. I will certainly check out the links provided. And I hope it's okay to add this question here, but what does Grothendieck mean by "modular multiplicities"? Is he referring to stacks? – Anton Hilado Feb 05 '16 at 13:11

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