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Apparently in preparation for the upcoming workshop on "Interuniversal Teichmüller Theory" in Kyoto in two weeks, which is intended to bring more light into Mochizukis proposed proof of the $abc$ conjecture and the new theory it comes with, there has appeared some new paper from Mochizuki titled The Mathematics of mutually alien copies: from gaussian integrals to inter-universal Teichmüller theory. Is there any progress on the matter connected with this work? For example, it seems that among other things one of the concepts introduced is something like a generalised Frobenius morphism that works for all primes. Can anyone comment on this? (There have been already questions here along that line, however that was before the new paper from July 2016).

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Raphael J.F. Berger
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    The theta link (and the arithmetic Kodaira-Spencer morphism, which are kind of related) is a kind of Frobenius for the function field case. You can see this as a descent data over the field of one element (I think this is not written anywhere, though). There's the point of view of p-adic Teichmuller theory, where the log-link is the analogous of a Frobenius. About the verification of the theory, there are some comments in http://www.kurims.kyoto-u.ac.jp/~motizuki/Questions%20and%20Comments%20on%20IUT.pdf – user40276 Jul 05 '16 at 20:45
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    I'm sorry but I voted to close since I'm tired of the same Mochizuki questions. When he writes something comprehensible, I'm sure people will be able to comment. Maybe something will happen from the Kyoto meeting (based on past experience, I am not optimistic). But until the dust clears (if it does), questions on the Mochizuki papers don't seem to go anywhere. – Lucia Jul 06 '16 at 07:34
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    I see your point, actually my question was if the dust clears. So you say in essence you know that the dust has not cleared. Is this an opinion or is it based on reasoning? – Raphael J.F. Berger Jul 06 '16 at 08:46
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    Having taken a brief look at the cited paper, I think it is at least very badly written down. -- Unless the other works of Mochizuki on the abc conjecture show much cleaner argumentation, I find it hard to believe that they give a hundreds-of-pages-long proof without very substantial errors. – Stefan Kohl Jul 06 '16 at 09:39
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    Maybe you can edit your question to ask something more specific and not just about the progress (which is too polemic and will lead nowhere). For instance, the analogy with the Frobenius morphism would be a good question. I would like to see a clean explanation of this and how to relate the KS morphism (which gives another F_1) with the theta-link in a formal way. Maybe Minhyong Kim or other people more acquainted with anabelian stuff will know this. – user40276 Jul 06 '16 at 21:31
  • OK I will try to specify my question, please hold the line. – Raphael J.F. Berger Jul 06 '16 at 21:37
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    What specifically is 'very badly' written in the expository paper? I think it lays out the strategy quite well (well beyond just the integral analogy and explaining the language he uses), which gives at least some starting points for the reading of the other papers. I was not able to find anything which is wrong or written badly and I found it well readable, even for somebody far from an expert. – user_1789 Aug 01 '16 at 09:38

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