The equivariant Tamagawa Number Conjecture for abelian extensions of imaginary quadratic fields

Dominik Bullach; Martin Hofer

The equivariant Tamagawa Number Conjecture for abelian extensions of imaginary quadratic fields

Dominik Bullach^*, Martin Hofer

^*Corresponding author for this work

Universität der Bundeswehr München

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Abstract

We prove the Iwasawa-theoretic version of a conjecture of Mazur–Rubin and
Sano in the case of elliptic units. This allows us to derive the p-part of the equivari-
ant Tamagawa Number Conjecture at s = 0 for abelian extensions of imaginary
quadratic fields in the semi-simple case and, provided that a standard μ-vanishing
hypothesis is satisfied, also in the general case.

Original language	English
Number of pages	37
Journal	DOCUMENTA MATHEMATICA
Publication status	Accepted/In press - 20 Feb 2023

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title = "The equivariant Tamagawa Number Conjecture for abelian extensions of imaginary quadratic fields",

abstract = "We prove the Iwasawa-theoretic version of a conjecture of Mazur–Rubin andSano in the case of elliptic units. This allows us to derive the p-part of the equivari-ant Tamagawa Number Conjecture at s = 0 for abelian extensions of imaginaryquadratic fields in the semi-simple case and, provided that a standard μ-vanishinghypothesis is satisfied, also in the general case.",

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T1 - The equivariant Tamagawa Number Conjecture for abelian extensions of imaginary quadratic fields

AU - Bullach, Dominik

AU - Hofer, Martin

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N2 - We prove the Iwasawa-theoretic version of a conjecture of Mazur–Rubin andSano in the case of elliptic units. This allows us to derive the p-part of the equivari-ant Tamagawa Number Conjecture at s = 0 for abelian extensions of imaginaryquadratic fields in the semi-simple case and, provided that a standard μ-vanishinghypothesis is satisfied, also in the general case.

AB - We prove the Iwasawa-theoretic version of a conjecture of Mazur–Rubin andSano in the case of elliptic units. This allows us to derive the p-part of the equivari-ant Tamagawa Number Conjecture at s = 0 for abelian extensions of imaginaryquadratic fields in the semi-simple case and, provided that a standard μ-vanishinghypothesis is satisfied, also in the general case.

M3 - Article

SN - 1431-0635

JO - DOCUMENTA MATHEMATICA

JF - DOCUMENTA MATHEMATICA

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The equivariant Tamagawa Number Conjecture for abelian extensions of imaginary quadratic fields

Abstract

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