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nLab > Latest Changes: Langlands correspondence

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 18th 2014

    gave Langlands correspondence an actual Idea-section.

    (Am in a rush and on a horrible wifi connection. Need to proof-read and add more links later.)

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 19th 2014
    • (edited Jul 19th 2014)

    We must add pointers to the excellent reviews of the state of the art given in the ICM talks by Taylor at ICM 2002 and by Michael Harrsis for ICM 2014 (already available from his website).

    (Myself, I am quasi offline until tomorrow.)

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 20th 2014

    I added those references, including the longer version of Taylor’s talk.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJul 20th 2014

    Thanks!

    • CommentRowNumber5.
    • CommentAuthorRodMcGuire
    • CommentTimeJul 20th 2014
    • (edited Jul 20th 2014)

    Right now I am getting a persistent error on http://ncatlab.org/nlab/show/Langlands%20correspondence. (I’ve gotten this message in the past but it disappears on reload). The 500 error says

    Application error (Apache)

    Please report this on the nForum (in the Technical category), giving as precise details as you can as to what triggered the error.

    also reported in Techinical: application error

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 21st 2014

    I added a link to the IAS page on Langlands’ work, and moved the link to the sunsite.ubc.ca page to one that is higher up in the tree.

    I also added a link to the specific page for the Letter to Weil, and to the sunsite.ubc.ca page, which is not identical.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeAug 28th 2014

    I have expanded the Idea section by adding paragraphs on the other parts of the conjecture, which had not been mentioned in the entry before: the generalization to arbitrary reductive groups and the “functoriality” statement.

    What I find curious is that looking at it all after the dust has settled, it is not actually so much the correspondence between Galois representations and automorphic representations that the heart of the conjecture is about. Rather, the automorphic representations seem more a technical intermediate step in order to construct the automorphic L-functions.

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