On characteristic polynomials of certain Iwasawa modules

Abstract

Let K-infinity/K be the cyclotomic Z(p)-extension of a number field K. In this paper, we consider generalized versions of conjectures of Leopoldt, Coates-Lichtenbaum, and Gross, which predict the exact orders of zeros of characteristic polynomials of Iwasawa modules naturally attached to K-infinity/K at Y = 0. We show that these conjectures are closely related to each other when K is a CM field. As a corollary, when K is an abelian extension of Q, we prove a theorem generalizing both Coates-Lichtenbaum and Gross-Leopoldt conjectures from known results.