Iwasawa Theory, Projective Modules, and Modular Representations

This paper shows that properties of projective modules over a group ring $mathbf{Z}_p[Delta]$, where $Delta$ is a finite Galois group, can be used to study the behavior of certain invariants which occur naturally in Iwasawa theory for an elliptic curve $E$. Modular representation theory for the group $Delta$ plays a crucial role in this study. It is necessary to make a certain assumption about the vanishing of a $mu$-invariant. The author then studies $lambda$-invariants $lambda_E(sigma)$, where $sigma$ varies over the absolutely irreducible representations of $Delta$. He shows that there are non-trivial relationships between these invariants under certain hypotheses.