Some remarks on finite submodules of the unramified Iwasawa module of totally real fields

Let k be a number field and p a prime number. It is conjectured by Greenberg that the Iwasawa λ- and μ-invariants of the cyclotomic Zₚ-extension of k always vanish if k is totally real. In this article, we will discuss a weak version of Greenberg’s conjecture, and give results analogous to Greenberg’s and Ozaki’s results.