Abstract
In §§ 1–3, we will consider exclusively local fields (assumed to be commutative). We denote by K a local field and by K’ an algebraic extension of K of finite degree n over K. If K is an R-field and K’ ≠ K, we must have K = R, K’ = C, n = 2; then, by corollary 3 of prop. 4, Chap. III–3, Tr C/R (x) = x+x̄ and N C/R (x)= xx̄; Tr C/R maps C onto R, and N C/R maps C× onto R ×+ , which is a subgroup of R× of index 2.
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© 1967 Springer-Verlag Berlin · Heidelberg
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Weil, A. (1967). Traces and norms. In: Basic Number Theory. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-00046-5_8
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DOI: https://doi.org/10.1007/978-3-662-00046-5_8
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