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Iwasawa Theory, Projective Modules, and Modular Representations (Memoirs of the American Mathematical Society)

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Description

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. About the Author Ralph Greenberg, University of Washington, Seattle, WA

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paperback
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Amazon UK
Release Date
30 April 2011
Listed Since
21 February 2011

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