Iwasawa Theory, Projective Modules, and Modular Representations - Ralph Greenberg

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Résumé :
This paper shows that properties of projective modules over a group ring dollars\mathbf{Z}_p[\Delta] dollars, where dollars\Delta dollars 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 dollarsE dollars. Modular representation theory for the group dollars\Delta dollars plays a crucial role in this study. It is necessary to make a certain assumption about the vanishing of a dollars\mu dollars-invariant. The author then studies dollars\lambda dollars-invariants dollars\lambda_E(\sigma) dollars, where dollars\sigma dollars varies over the absolutely irreducible representations of dollars\Delta dollars. He shows that there are non-trivial relationships between these invariants under certain hypotheses.