Preliminaries on Adele-Geometry

Part of the Progress in Mathematics book series (PM, volume 23)


We always denote by k a field of algebraic numbers or a field of algebraic functions of one variable over a finite constant field. We denote by k the completion of k with respect to a valuation v of k; if v is discrete, we use often the notation p and denote by \( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}\to {o} _p \) the ring of p-adic integers in kp. We denote by S any finite set of valuations which contains all the non discrete valuations (infinite places).


Galois Group Inductive Limit Galois Extension Generic Section Affine Variety 
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Copyright information

© Birkhäuser Boston 1982

Authors and Affiliations

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

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