### Greenberg's conjecture and cyclotomic towers, by David C. Marshall

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.

David C. Marshall <marshall@math.mcmaster.ca>