Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
  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.

  3. 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.

  4. 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

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

    Anonymous

    v1, current

  6. Fixing spelling errors

    Anonymous

    v1, current

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

    Anonymous

    v1, current

  8. 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