We develop an explicit “higher-rank” Iwasawa theory for zeta elements associated to the multiplicative group over abelian extensions of number fields. We show this theory leads to a concrete new strategy for proving special cases of the equivariant Tamagawa number conjecture and, as a first application of this approach, we prove new cases of the conjecture over natural families of abelian CM-extensions of totally real fields for which the relevant p-adic L-functions possess trivial zeroes.
- Equivariant tamagawa number conjecture
- Higher-rank iwasawa main conjecture
- Rubin-stark conjecture
ASJC Scopus subject areas
- Algebra and Number Theory