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manuscripta mathematica

, Volume 102, Issue 2, pp 187–209 | Cite as

Conjectures de Greenberg et extensions¶pro-p-libres d'un corps de nombres

  • Arthur Lannuzel
  • Thong Nguyen Quang Do

Abstract:

For an algebraic number field k and a prime number p (if p=2, we assume that μ4k), we study the maximal rank ρ p of a free pro-p-extension of k. This problem is related to deep conjectures of Greenberg in Iwasawa theory. We give different equivalent formulations of these conjectures and we apply them to show that, essentially, ρ k =r 2(k)+1 if and only if k is a so-called p-rational field.

Mathematics Subject Classification (1991):11R23, 11R32, 11R34 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Arthur Lannuzel
    • 1
  • Thong Nguyen Quang Do
    • 1
  1. 1.Université de Franche-Comté, UMR 6623 CNRS, Laboratoire de Mathématiques, 16, route de Gay, 25030 Besançon Cédex, France.¶e-mail: lannuz@math.univ-fcomte.fr; nguyen@math.univ-fcomte.frFR

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