Iwasawa Theory, projective modules, and modular representations

Abstract

This paper shows that properties of projective modules over a group ring Zp[∆], where ∆ 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 ∆ plays a crucial role in this study. It is necessary to make a certain assumption about the vanishing of a μ-invariant. We then study λ-invariants λE(σ), where σ varies over the absolutely irreducible representations of ∆. We show that there are non-trivial relationships between these invariants under certain hypotheses. 2000 Mathematics Subject Classification: Primary 11G05, 11R 23 Secondary 20C15, 20C20