Galois module structure of (ℓ<sup> <i>n</i> </sup> )th classes of fields
Galois module structure of (ℓ<sup> <i>n</i> </sup> )th classes of fields
In this paper, we use the Merkurjev–Suslin theorem to determine the structure of arithmetically significant Galois modules that arise from Kummer theory. Let K be a field of characteristic different from a prime ℓ, n be a positive integer, and suppose that K contains the (ℓn)th roots of unity. Let …