Part of the Graduate Texts in Mathematics book series (GTM, volume 110)
Let χ be a character of the idele classes C k (or equivalently, of J k ,vanishing on k*),that is a continuous homomorphism
and assume in addition throughout this section that χ has finite period. Then the kernel H χ of χ is a closed subgroup of finite index, which is therefore open, and has a class field denoted by K χ.
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© Springer Science+Business Media New York 1994