On characteristic polynomials of certain Iwasawa modules

Let K_∞/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_∞/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.