A B S T R A C T
This paper concerns the relation between the Lifted Root Number Conjecture, as introduced
in [GRW2], and a new equivariant form of Iwasawa theory. At present, a main conjecture
of equivariant Iwasawa theory is formulated, and its equivalence to the Lifted Root Num-
ber Conjecture is shown subject to the validity of a semi-local version of the Root Number
Conjecture, which itself is proved in the case of a tame extension of real abelian fields.
2000 Mathematics Subject Classification:
Primary 11R23, 11R27, 11R32, 11R33, 11R37, 11R42, 11S20, 11S23, 11S31, 11S40
Secondary 11-02, 11R18, 11R65
Key words and Phrases :
Galois module structure, global units, Chinburg's Root Number Conjecture, the Lifted Root
Number Conjecture, Iwasawa theory, /-adic L-functions, class field theory, cyclotomic fields,
integral representations
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