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 complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration 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 nforum 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).

nLab > Latest Changes: modularity theorem

Bottom of Page

1 to 8 of 8

  1.  

  1. adding contents

    Anonymous

    diff, v4, current

  2. I have hyperlinked the two terms in

    …with a conductor N EN_E, there is a cusp form…

    We currently do have a puny page for conductor, though I am not sure if that’s even what you need here. We don’t yet have a page for cusp form, but eventually we should.

    Anonymous

    diff, v4, current

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 6th 2022

    The history is currently wrong: Wiles and Taylor–Wiles only proved the semi-stable case. Breuil–Conrad–Diamond–Taylor proved the full theorem.

    Also the page doesn’t define a p(E)a_p(E)!

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 7th 2022

    Corrected attribution of full theorem.

    diff, v5, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 7th 2022

    replaced

    was proved by Breuil, Conrad, Diamond and Taylor, published in 2001

    by

    was proved by Breuil, Conrad, Diamond & Taylor 2001

    Replaced

    Andrew Wiles with Richard Taylor proved the “semistable” case of the modularity theorem in 1997,

    by

    The “semistable” case of the modularity theorem was proven in Wiles 1995, Taylor & Wiles 1995.

    and added the respective references:

    But I don’t actually know which references should go here, this is just what I gather from looking around. If you really do want a reference from 1997 here, then please add it.

    In this vein, I have found (and have added now) the review

    • Gerd Faltings, The Proof of Fermat’s Last Theorem by R. Taylor and A. Wiles, Notices of the AMS (1995) [[pdf]]

    which, bizarrely, gives no reference to the work that is being reviewed.

    diff, v6, current

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 7th 2022

    I was mystified by the 1997 date too, I didn’t yet have time to give the canonical references. Perhaps there was an intermediate result?

    The Faltings article may have been written before the final publication in the Annals? Or else it was considered so famous it didn’t need a reference?

    • CommentRowNumber7.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 30th 2022

    Added “generalizations” section. Will add references later.

    diff, v7, current

    • CommentRowNumber8.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 30th 2022

    Added reference to Freitas-Le Hung-Siksek.

    diff, v8, current

1 to 8 of 8

  1.