Applications to Artin representations

  • Jean-Pierre Serre
Part of the Graduate Texts in Mathematics book series (GTM, volume 42)


Let E be a field complete with respect to a discrete valuation, let F/E be a finite Galois extension of E, with Galois group G, and assume for simplicity that E and F have the same residue field. If s ≠ 1 is an element of G and if π is a prime element of F, put
$$ _{{i_G}}(s) = {v_F}(s(\pi ) - \pi ), $$
where vF denotes the valuation of F, normalized so that vF(π) = 1.


Elliptic Curf Galois Group Prime Element Residue Field Residue Characteristic 
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Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • Jean-Pierre Serre
    • 1
  1. 1.Chaire d’algèbre et géométrieCollège de FranceParisFrance

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