Riv.Mat.Univ.Parma (7) 3* (2004)
ANDREA BANDINI
Greenberg's conjecture for multiple Zp-extensions
Pages: 151-158
Received: 20 January 2004
Mathematics Subject Classification (2000): 11R23
Abstract:
Let k~ be the compositum of all the Z
p-extensions
of a number field k. We shall consider fields k with
Gal(k/Q) ~
(Z/2Z)n. Building on known results for
quadratic fields we shall show that the Galois group of the
maximal abalian unramified pro-pextension of k~ is
pseudo-null for several such
k's, thus confirming a conjecture of Greenberg.
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