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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 23rd 2014
    • (edited Jul 23rd 2014)

    added the definition of idele class group to group of ideles, with a brief pointer to its role in the moduli stack of line bundles. Added both then to the function field analogy – table

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 25th 2014

    added the statement of the strong approximation theorem for ideles.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 25th 2014
    • (edited Aug 25th 2014)

    added the statement of the product formula

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 25th 2014
    • (edited Aug 25th 2014)

    So ideles are defined from adeles, but the way this page begins it sounds like you can have a 𝕀 \mathbb{I}_{\mathbb{Z}}, i.e., ideles from the integral adeles. And yet by definition 2, we see “The same definition holds …” and it just talks about 𝕀 𝕂\mathbb{I}_{\mathbb{K}} for fields thereafter.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeAug 25th 2014

    Thanks for catching this. That definition of the integral adeles has no purpose on the page, I have removed it now. Probably I (or somebody) accidentally copy-and-pasted this over when the discussion of ideles was split off from that of adeles, at some point.

    I have also added some more {}_{\mathbb{Q}}-subscripts, for clarity.

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