Abstract
By a cyclic layer of a finite Galois extension,E/K, of fields one means a cyclic extension,L/F, of fields whereE⊇L⊇F⊇K. LetC(E/K) denote the subgroup of the relative Brauer group, Br(E/K), generated by the various subgroups cor(Br(L/F)) asL/F ranges over all cyclic layers ofE/K and where cor denotes the corestriction map into Br(E/K). We show that forK global, [Br(E/K) :C(E/K)]<∞ and we produce examples whereC(E/K)≠Br(E/K).
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In memory of S.A. Amitsur, our teacher, friend, collaborator, and inspiration.
Supported in part by NSA Grant No. MDA904-95-H-1054.
Supported in part by NSA Grant No. MDA904-95-H-1022.
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Fein, B., Schacher, M. Sums of corestrictions of cyclic algebras. Israel J. Math. 96, 243–258 (1996). https://doi.org/10.1007/BF02785541
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DOI: https://doi.org/10.1007/BF02785541