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Has anyone here looked at the definition of anabelioids given by Mochizuki in his work on the various forms of the Grothendieck section conjecture. In his paper ‘The geometry of anabelioids’ he has various notions (see p. 26 for a span?), and I have a feeling that some of the time he renames concepts that I know and love and it is not clear why. Has anyone read any of this? I know the profinite group, Galois theoretic background a bit but I am getting lost in this!
I am, in part, wondering what parts of this should be summarised in the Lab.
(Edit: I forgot to say that I did not see where anabelian came into his definition of anabelioids, although I must plead guilty to just skimming the pages.)
Has anyone here looked at the definition of anabelioids given by Mochizuki in his work
[…] I did not see where anabelian came into his definition of anabelioids
Let’s see. On page 9 a “connected anabelioid” is defined to be a category of -sets for a profinite group.
On p. 13, remark 1.1.4.1 he says why he chose to call these “anabelioids”: because as toposes they are entirely determined by their fundamental group.
A traditional term expressing the same idea is, of course, that these are the classifying toposes for that group.
I could not see how what he gave as a version of the conjecture was more than a fairly obvious observation! I agree that these things are just the classifying toposes of the corresponding profinite groups, and I do not see what he gains by not using that terminology!
Yeah, same for me. I am not sure what to make of it.
I believe it’s meant to be alluding to fundamental groupoids in anabelian geometry.
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