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nLab > Latest Changes: modularity theorem

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  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

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