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nLab > Latest Changes: Mochizuki's proof of abc

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  1. this page seems to have no discussion page

    Anonymous

    diff, v8, current

    • CommentRowNumber2.
    • CommentAuthorGuest
    • CommentTimeJun 21st 2021
    This page needs a complete overhaul, as the last time this page was updated was in 2013. Most important is probably including Corollary 3.1.2 and the proofs by Scholze and Styx why Mochizuki's proof of Corollary 3.1.2 is incorrect. There are other remarks as well, including one from David Roberts from 2018 if I recall correctly.

    One might also want to split of corollary 3.1.2 into its own article, as there have been mathematicians treating it like another algebraic geometry/number theory conjecture such as Taylor Dupuy in

    https://arxiv.org/abs/2004.13228
    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 22nd 2021

    A minor remark: 3.12, not 3.1.2

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 22nd 2021
    • (edited Jun 22nd 2021)

    I have tried to give the entry a tad more structure. It used to be a little odd with a humongous quote of Dimitriov followed by a single reference to Scholze&Stix. I gather from this that the intent of the entry is to collect discussion of Mochizuki’s proof by various authors. To bring this out, more clearly, I have made a section header “Reactions” with sub-sections for Dimitrov and for Scholze&Stix.

    Also I added Dimitrov’s comment as an item to the list of references, so that it can be referred to as usual. This way we also don’t need a disclaimer that Dimitrov is not the author of this nnLab page, for it’s more clear now that his text is being referenced and quoted

    I think these edits help bring out the point of this entry better. But it still remains an oddly unbalanced entry, in how it quotes one of its references at immense lengths and has not a single word to say about its second reference.

    I’d suggest:

    • Either somebody feels ambitious about this page – then there ought to be (a) more substantial discussion in the Idea-section, (b) some editorial comments to go with the huge quote by Dimitrov and (c) a minimum of text to go with the pointer to Scholze & Stix.

    • Or if nobody feels ambitious about this page, then it might be better to remove that huge quote and have the entry admit that it remains a stub offering nothing but a (short) link list to commentary on Mochizuki’s proof.

    diff, v10, current

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