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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 $\mathbb{I}_{\mathbb{Z}}$, i.e., ideles from the integral adeles. And yet by definition 2, we see “The same definition holds …” and it just talks about $\mathbb{I}_{\mathbb{K}}$ 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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