Places of A-fields

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


By an algebraic number-field, it is customary to understand a finite algebraic extension of Q. One main object of this book, and of number-theory in general, is to study algebraic number-fields by means of their embeddings into local fields. In the last century, however, it was discovered that the methods by which this can be done may be applied with very little change to certain fields of characteristic p >1; and the simultaneous study of these two types of fields throws much additional light on both of them. With this in mind, we introduce as follows the fields which will be considered from now on:

Definition 1. A field will be called an A -field if it is either a finite algebraic extension of Q or a finitely generated extension of a finite prime field F p , of degree of transcendency 1 over F p .


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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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