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, Volume 72, Issue 1, pp 307–324 | Cite as

Lois de reciprocite primitives

  • Nguyen Quang Do Thong


For an algebraic number fieldK containing roots of unity of orderp m (p a prime), we study a new kind of reciprocity law, called “primitive”, which allows us, when it exists, to express wild Hilbert symbols of orderp m in terms of a (uniformly) finite set of tame symbols. A sufficient condition for existence is the nullity of thep-group of classes ofp-ideals ofK. Applications are given to the description of the Galois group of the maximal prop-extension ofK which is unramified outside some finite set of primes containingp.


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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Nguyen Quang Do Thong
    • 1
  1. 1.URA 741 CNRS Laboratoire de MathématiquesUniversité de Franche-ComtéBESANCON Cédex

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