Memoirs of the American Mathematical Society 2011; 185 pp; softcover Volume: 211 ISBN10: 082184931X ISBN13: 9780821849316 List Price: US$83 Individual Members: US$49.80 Institutional Members: US$66.40 Order Code: MEMO/211/992
 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 nontrivial relationships between these invariants under certain hypotheses. Table of Contents  Introduction
 Projective and quasiprojective modules
 Projectivity or quasiprojectivity of \(X_{E}^{\Sigma_0}(K_{\infty})\)
 Selmer atoms
 The structure of \(\mathcal{H}_v(K_{\infty}, E)\)
 The case where \(\Delta\) is a \(p\)group
 Other specific groups
 Some arithmetic illustrations
 Selfdual representations
 A duality theorem
 \(p\)modular functions
 Parity
 More arithmetic illustrations
 Bibliography
