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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJul 23rd 2014
   • (edited Jul 23rd 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded 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]]_

   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

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeAug 25th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the statement of the [strong approximation theorem](http://ncatlab.org/nlab/show/group+of+ideles#StrongApproximationTheorem) for ideles.

   added the statement of the strong approximation theorem for ideles.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeAug 25th 2014
   • (edited Aug 25th 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the statement of the [product formula](http://ncatlab.org/nlab/show/group+of+ideles#ProductFormula)

   added the statement of the product formula

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeAug 25th 2014
   • (edited Aug 25th 2014)
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   Author: David_Corfield
   Format: MarkdownItexSo 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.

   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.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeAug 25th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks 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.

   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.