Capitulation in the cyclotomic ℤ2 extension of CM number fields.

Let 𝕂n be the intermediate steps in the cyclotomic ℤp-extension of a CM number field 𝕂. For p ⧧ 2 the minus part of the p-class groups is given by An− = 1/2 (1 − j) An. We will give a new definition of the minus part for p = 2 and will prove that there is no finite submodule in lim∞← n An−. Furthermore we will show that μ = 0 if and only if μ − = 0 in this new definition. [ABSTRACT FROM AUTHOR]