Greenberg's conjecture and cyclotomic towers

Abstract

We describe Greenberg's pseudo-null conjecture, and prove a result describing conditions under which the pseudo-null conjecture for a number field K implies the conjecture for finite extensions of K. We then apply the result to the cyclotomic Z p -tower above a cyclotomic field of prime roots of unity, verifying the conjecture for a large class of cyclotomic fields.

K_2 et conjecture de Greenberg dans les \mathbb{Z}_p-extensions multiples

“…En fait, il suffit de remplacer i = 0 par i = −2 pour obtenir une preuve qui est indépendante de la conjecture de Leopoldt. On peut aussi consulter [15], [14] ou [9].…”