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Greenberg's conjecture and cyclotomic towers

David C. Marshall
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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 $\mathbb{Z}_p$-tower above a cyclotomic field of prime roots of unity, verifying the conjecture for a large class of cyclotomic fields.

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David C. Marshall. 2001-09-25. Greenberg's conjecture and cyclotomic towers. https://arxiv.org/abs/math/0109229

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