Abstract
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.
Original language | English |
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Pages (from-to) | 1527-1571 |
Number of pages | 45 |
Journal | Algebra and Number Theory |
Volume | 11 |
Issue number | 7 |
Early online date | 7 Sept 2017 |
DOIs | |
Publication status | Published - 7 Sept 2017 |
Keywords
- Equivariant tamagawa number conjecture
- Higher-rank iwasawa main conjecture
- Rubin-stark conjecture