Elliptic Curves, Modular Forms and Iwasawa Theory
Elliptic Curves, Modular Forms and Iwasawa Theory
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椭圆曲线、模形式和岩泽理论
DOI：
10.1007/978-3-319-45032-2_8
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Kakde M
中科院分区：
文献类型：
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作者：
Kakde M
求一个奇素数和一个齐李群。对于Iwasawa代数，由于Ritter-Weiss和Kato的工作（由作者推广），在g的阿贝尔子商的Iwasawa代数的元素之间的同余方面得到了很好的理解。在前一种方法中，我们需要处理g的所有阿贝尔子商，而在加藤的方法中，我们可以处理g的某个精心选择的阿贝尔子商子类。例如，在[11]中对元abel pro-pgroup进行了计算，但对于某些特殊的元abel pro-pgroup，这种描述只能对全实域的- adicl函数证明同余。通过改变阿贝尔子商的类别，在[12]中得到了一个不同的一般描述，并证明了在所有情况下全实域的- adicl函数的同余。在这篇文章中，我们提出了一种策略来获得关于何时的另一种描述。对此，计算就足够了。我们通过显式计算来演示该策略应该如何工作，这是最有趣的部分。
Letpbe an odd prime and letGbe ap-adic Lie group. The group, for the Iwasawa algebra, is well understood in terms of congruences between elements of Iwasawa algebras of abelian sub-quotients ofGdue to the work of Ritter-Weiss and Kato (generalised by the author). In the former one needs to work with all abelian subquotients ofGwhereas in Kato’s approach one can work with a certain well-chosen sub-class of abelian sub-quotients ofG. For instance in [11]was computed for meta-abelian pro-pgroupsGbut the congruences in this description could only be proved forp-adicL-functions of totally real fields for certain special meta-abelian pro-pgroups. By changing the class of abelian subquotients a different description of, for a generalG, was obtained in [12] and these congruences were proven forp-adicL-functions of totally real fields in all cases. In this note we propose a strategy to get an alternate description ofwhen. For this it is sufficient to compute. We demonstrate how the strategy should work by explicitly computing, the pro-ppart of, which is the most interesting part.