Iwasawa theory for abelian extensions over imaginary quadratic fields and elliptic units

研究了Brumer猜想与coats - sinnott猜想的关系。前者与数域的理想类群有关，后者与整数环的k群有关。在论文《A note on the Coates-Sinnott conjecture， Bulletin of the London, 41,613 -620, 2009》中，我证明了前者猜想在某些假设下隐含后者猜想。在另一篇论文“On some exact sequences In theory of cyclotomic fields, Journal of Algebra, 2000,4156 -4177”中，我证明了一些与Iwasawa模的正负部分相关的精确序列的存在性。在此基础上，提出了关于环切场的整数环的k群的一些猜想，并利用环切单位和高斯和描述了一阶的上同群。在研究的最后，我考虑了一般的阿贝尔数域和虚二次域上的阿贝尔扩展。

I studied the relation between Brumer conjecture and Coates-Sinnott conjecture. The former is related to ideal class groups of number fields, and the latter is related to K-groups of the rings of integers. In my paper "A note on the Coates-Sinnott conjecture, Bulletin of the London Mathematical Society 41, 613-620, 2009", I proved that the former conjecture implies the latter conjecture under some assumptions. In another paper "On some exact sequences in the theory of cyclotomic fields, Journal of Algebra 320, 4156-4177, 2008", I showed the existence of some exact sequences which relate both the plus part and the minus part of Iwasawa modules. Furthermore, I formulated some conjecture about K-groups of the rings of integers of cyclotomic fields, and described an order of etale cohomology groups by using cyclotomic units and Gauss sums. At the end of the study, I considered general abelian number fields and abelian extensions over imaginary quadratic fields.