Let K a finite extension of Q(sub p), K(sub infinity)/K an extension with Galoisgroup G isomorphic Z(sub p sup r), and X the Galois group of the maximal abelian p-extension of K(sub infinity). The conjugation action of G on X gives rise to a Lambda-module structure, where Lambda is the Iwasawa algebra of bounded Z(sub p)-valued measures on G. In this paper, the authors define a non-degenerate sesqui-linear pairing a Lambda -modules X x X -> Lambda, where Lambda is the algebra of Z(sub p) (1)-valued measures on G (noncanonically isomorphic to Lambda as a Lambda-module). The pairing is obtained from the Hilbert pairing in a very simple way. Specifically, the authors show in Theorem 4.7 that the pairing is perfect when r > 2 and K(sub infinity)/K is quasi-regular when K(sub infinity)/K can be embedded in an extension of K whose Galois group is a free pro-p-group.
展开▼
