Greenberg's conjecture and cyclotomic towers

2001/09/25 by David C. Marshall, Marshall, David C.
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0109229

arxiv created 2001/09/25 · arxiv updated 2009/12/01

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.

Related

• Greenberg's conjecture and units in multiple Z_p-extensions
• A weak form of Greenberg's conjecture for the cyclotomic ℤ₂-extension of real quadratic fields
• Greenberg's conjecture for real quadratic fields and the cyclotomic ℤ₂-extensions
• Universal norms and Greenberg conjecture
• On Greenberg's generalized conjecture for families of number fields