虚二次域阿贝尔扩展的等变Tamagawa数猜想

IF 0.9 3区数学 Q2 MATHEMATICS

Documenta Mathematica Pub Date : 2021-02-02 DOI:10.4171/dm/907

Dominik Bullach, Martin Hofer

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引用次数: 2

摘要

在椭圆单位情况下，我们证明了Mazur—Rubin和Sano猜想的iwasawa理论版本。这允许我们在半简单情况下，对于虚二次域的阿贝尔扩展，在$s = 0$处推导出等变Tamagawa数猜想的$p$-部分，并且在满足标准$\mu$-消失假设的情况下，也在一般情况下。

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The equivariant Tamagawa number conjecture for abelian extensions of imaginary quadratic fields

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 equivariant Tamagawa number conjecture at $s = 0$ for abelian extensions of imaginary quadratic fields in the semi-simple case and, provided that a standard $\mu$-vanishing hypothesis is satisfied, also in the general case.

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来源期刊

Documenta Mathematica 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： DOCUMENTA MATHEMATICA is open to all mathematical fields und internationally oriented Documenta Mathematica publishes excellent and carefully refereed articles of general interest, which preferably should rely only on refereed sources and references.