Let be a number field. For each finite prime of , let denote the valuation ring of the completion of at . The adèle group of is defined to be the restricted direct product of the collection of locally compact additive groups over all primes of (both finite primes and infinite primes), with respect to the collection of compact open subgroups defined for all finite primes .
defined for , where denotes the image of in under the embedding . Note that for all but finitely many , so that the element is sent under the above definition into the restricted direct product as claimed.
|Date of creation||2013-03-22 12:39:31|
|Last modified on||2013-03-22 12:39:31|
|Last modified by||djao (24)|
|Defines||group of adèles|