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nLab > Latest Changes: Mochizuki's corollary 3.12

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  1. stub article on Mochizuki’s corollary 3.1.2

    Anonymous

    v1, current

  2. adding more references and cross-linked with Szpiro’s conjecture

    Anonymous

    v1, current

    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 21st 2021

    Mochizuki’s corollary 3.1.2 is a conjecture by Shinichi Mochizuki in number theory and algebraic geometry that first appeared in his incorrect proof of the abc conjecture.

    Does “incorrect” refer to some early mistakes that were later fixed? Rephrasing to indicate this may be appropriate.

  4. Actually called Mochizuki’s Corollary 3.12

    Anonymous

    v1, current

    • CommentRowNumber5.
    • CommentAuthorGuest
    • CommentTimeJun 21st 2021
    Dmitri Pavlov wrote:

    > Does “incorrect” refer to some early mistakes that were later fixed? Rephrasing to indicate this may be appropriate.

    "incorrect" refers to the errors that Peter Scholze and Jakob Stix found in the proof of the corollary that to the best of my knowledge has not been adequetely addressed by Shinichi Mochizuki. The two of them wrote their findings in an article called _Why abc is still a conjecture_ which could be found [here](https://ncatlab.org/nlab/files/why_abc_is_still_a_conjecture.pdf).
    • CommentRowNumber6.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 21st 2021

    “incorrect” refers to the errors that Peter Scholze and Jakob Stix found in the proof of the corollary that to the best of my knowledge has not been adequetely addressed by Shinichi Mochizuki.

    Remark 3.8.3 in https://arxiv.org/abs/2004.13108v2 suggests otherwise.

  7. Clarified what I meant when I said Mochizuki’s proof is incorrect: it is not the proofs of Szpiro’s conjecture from Mochizuki’s corollary 3.1.2, but rather the proof of corollary 3.1.2 itself from inter-universal Teichmüller theory.

    Anonymous

    v1, current

  8. Mentioned relationship between Mochizuki’s corollary 3.12 and Szpiro’s conjecture.

    Anonymous

    v1, current

  9. Fixing spelling errors

    Anonymous

    v1, current

  10. Dupuy and Hilado also call the conjecture “Mochizuki’s inequality”

    Anonymous

    v1, current

  11. Adding preprint

    • Kirti Joshi, Construction of Arithmetic Teichmuller Spaces III: A ‘Rosetta Stone’ and a proof of Mochizuki’s Corollary 3.12 (arXiv:2401.13508)

    Sam Wilson

    diff, v4, current

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