TY - JOUR

T1 - On Iwasawa theory, zeta elements for Gm, and the equivariant Tamagawa number conjecture

AU - Burns, David

AU - Kurihara, Masato

AU - Sano, Takamichi

N1 - Funding Information:
The second author would like to thank C. Greither very much for discussion with him on topics related to the subjects in Section 3E and Section 4B. He also thanks J. Coates heartily for his various suggestions on the exposition of this paper. The third author would like to thank Seidai Yasuda for his encouragement. The second and the third authors are partially supported by JSPS core-to-core program, “Foundation of a Global Research Cooperative Center in Mathematics focused on Number Theory and Geometry”.
Publisher Copyright:
© 2017 Mathematical Sciences Publishers.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Equivariant tamagawa number conjecture

KW - Higher-rank iwasawa main conjecture

KW - Rubin-stark conjecture

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U2 - 10.2140/ant.2017.11.1527

DO - 10.2140/ant.2017.11.1527

M3 - Article

AN - SCOPUS:85029434451

SN - 1937-0652

VL - 11

SP - 1527

EP - 1571

JO - Algebra and Number Theory

JF - Algebra and Number Theory

IS - 7

ER -