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 -adic -functions possess trivial zeroes.
Citation
David Burns. Masato Kurihara. Takamichi Sano. "On Iwasawa theory, zeta elements for $\mathbb{G}_{m}$, and the equivariant Tamagawa number conjecture." Algebra Number Theory 11 (7) 1527 - 1571, 2017. https://doi.org/10.2140/ant.2017.11.1527
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