The Hasse norm principle for elementary abelian extensions

Horie, Mitsuko

doi:10.1090/S0002-9939-1993-1139477-1

The Hasse norm principle for elementary abelian extensions
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Proc. Amer. Math. Soc. 118 (1993), 47-56 Request permission

Abstract:

Let $K/k$ be an elementary abelian extension of finite algebraic number fields. The Hasse norm principle for $K/k$ and its relation to the Hasse norm principles for all proper subextensions of $K/k$ will be discussed. The central class field of $K/k$ with $k = \mathbb {Q}$ will also be studied.

References

Dennis A. Garbanati, The Hasse norm theorem for non-cyclic extensions of the rationals, Proc. London Math. Soc. (3) 37 (1978), no. 1, 143–164. MR 491599, DOI 10.1112/plms/s3-37.1.143
Frank Gerth III, The Hasse norm principle for abelian extensions of number fields, Bull. Amer. Math. Soc. 83 (1977), no. 2, 264–266. MR 422200, DOI 10.1090/S0002-9904-1977-14297-3

Beweis eines Satzes und Wiederlung einer Vermutung über das allgemeine Normenrestsymbol

Mitsuko Horie, On central extensions of elementary abelian fields, J. Number Theory 36 (1990), no. 1, 95–107. MR 1068676, DOI 10.1016/0022-314X(90)90008-F
Mitsuko Horie, The Hasse principle for elementary abelian fields, Mem. Fac. Sci. Kyushu Univ. Ser. A 45 (1991), no. 1, 41–54. MR 1101763, DOI 10.2206/kyushumfs.45.41
Michael J. Razar, Central and genus class fields and the Hasse norm theorem, Compositio Math. 35 (1977), no. 3, 281–298. MR 466073
J. T. Tate, Global class field theory, Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), Thompson, Washington, D.C., 1967, pp. 162–203. MR 0220697