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Preliminaries on Adele-Geometry

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

Abstract

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).

Keywords

Galois Group Inductive Limit Galois Extension Generic Section Affine Variety 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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