Riv.Mat.Univ.Parma (7) 3* (2004)


Greenberg's conjecture for multiple Zp-extensions

Pages: 151-158
Received: 20 January 2004   
Mathematics Subject Classification (2000): 11R23


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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