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Iwasawa Theory, Projective Modules, and Modular Representations
Ralph Greenberg
出版American Mathematical Soc., 2010
主題Mathematics / Algebra / AbstractMathematics / Geometry / GeneralMathematics / Geometry / AlgebraicMathematics / Number Theory
ISBN082184931X9780821849316
URLhttp://books.google.com.hk/books?id=VknVAwAAQBAJ&hl=&source=gbs_api
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註釋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.