在全实数域上Gm的高阶欧拉系统

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2023-01-25 DOI:10.1353/ajm.2023.0001

Ryotaro Sakamoto

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引用次数: 2

摘要

摘要：本文利用Stickelberger元素构造了一个全实域上$Bbb{G\}_m$的高阶Euler系统。构造的一个关键要素是概括特征理想的概念。在一定的技术假设下，我们证明了一个$p$分支Iwasawa模的所有更高拟合理想都是由与Stickelberger元素规范相关的分析不变量描述的。

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A higher rank Euler system for Gm over a totally real field

Abstract:In this paper, we construct a higher rank Euler system for $\\Bbb\{G\}_m$ over a totally real field by using Stickelberger elements. A key ingredient of the construction is to generalize the notion of the characteristic ideal. Under certain technical assumptions, we prove that all higher Fitting ideals of a certain $p$-ramified Iwasawa module are described by analytic invariants canonicallyassociated with Stickelberger elements.

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来源期刊

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.