The split prime μ-conjecture and further topics in Iwasawa theory

Abstract

The thesis is divided in three independent chapters, each focused on a different problem in Iwasawa theory. In Chapter 1 we prove the split prime μ-conjecture for abelian extensions of imaginary quadratic fields. In Chapter 2 we prove that whenever Greenberg's conjecture holds, there exists an isomorphism behind the class number formula for cyclotomic fields. In Chapter 3 we prove that the Leopoldt defect of a totally real number field can be encoded by a group of ideal classes and we study the structure of this group.