The torsion of p-ramified Iwasawa modules for [formula omitted]-extensions

Abstract

We will study the torsion of p-ramified Iwasawa modules of the Z p 2 -extension over imaginary quadratic fields k. In this article, we prove that the torsion is trivial except for one case under the assumption that the prime p does not divide the class number of k. We also study generalized Greenberg's conjecture for the prime 2 and imaginary quadratic fields.