  We begin a study of m-th Chern classes and m-th characteristic symbols for
Iwasawa modules which are supported in codimension at least m. This extends the
classical theory of characteristic ideals and their generators for Iwasawa
modules which are torsion, i.e., supported in codimension at least 1. We apply
this to an Iwasawa module constructed from an inverse limit of p-parts of ideal
class groups of abelian extensions of an imaginary quadratic field. When this
module is pseudo-null, which is conjecturally always the case, we determine its
second Chern class and show that it has a characteristic symbol given by the
Steinberg symbol of two Katz p-adic L-functions.
