Traces and norms

  • André Weil
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 144)


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 x onto R + x , which is a subgroup of R x of index 2.


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Copyright information

© Springer Science+Business Media New York 1973

Authors and Affiliations

  • André Weil
    • 1
  1. 1.The Institute for Advanced StudyPrincetonUSA

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