A note on Iwasawa invariants and the main conjecture

Abstract

We fix a rational prime p, possibly 2, and a CM field K. Let AK[infinity]- denote the minus component of the p-primary class group of K[infinity], the basic p-extension of K. The Pontryagin dual (AK[infinity]-)p is a noetherian, torsion p[[T]]-module whose characteristic polynomial we denote by f(T). Iwasawa's Main Conjecture relates the algebraically defined f(T) to an analytically defined power series F(T) given by a p-adic L-function. Using the analytic class number formula, we give evidence for it based on the Iwasawa invariants of f(T) and F(T). I would like to thank Benedict H. Gross for suggesting this approach.