Abstract

Abstract. A Kummer theory of division points over rank one Drinfeld A = Fq[T]- modules defined over global function fields was given. The results are in complete analogy with the classical Kummer theory of division points over the multiplicative algebraic group Gm defined over number fields. Let K be a number field and let ¯ K be a fixed algebraic closure of K. For any positive integer n, let µn be the group of n-th roots of unity in ¯ K. Let G(n) = Gal(K(µn)/K). For K = Q, G(n) ∼ = (Z/nZ) ∗ , and for any number field K, G(l) ∼ = (Z/lZ) ∗ for almost all prime numbers l.

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