Adelic algebraic group
In the case of G being an abelian variety, it presents a technical obstacle, though it is known that the concept is potentially useful in connection with Tamagawa numbers.is taken to be the subspace topology in AN, the Cartesian product of N copies of the adele ring.This was to formulate class field theory for infinite extensions in terms of topological groups.Chevalley (1951) defined the ring of adeles in the function field case, under the name "repartitions"; the contemporary term adèle stands for 'additive idèles', and can also be a French woman's name.The term adèle was in use shortly afterwards (Jaffard 1953) and may have been introduced by André Weil.The computation of Tamagawa numbers for semisimple groups contains important parts of classical quadratic form theory.