论文标题
关于CM场的理想班级组的注释
Notes on the dual of the ideal class groups of CM-fields
论文作者
论文摘要
在本文中，对于CM Abelian Extension $ K/K $的数字字段，我们提出了一个猜想，该猜想完全描述了$ t $ ray类$ k $的pontryagin dual的拟合理想，用于$ t $ t $ t $ primes的$ t $ t $ primes作为$ {\ rm gal all}（k/k/k/k）$ - 模块。在这里，我们强调我们考虑了整个班级组，并且不要丢弃刺激的素数（即，我们研究的对象不是班级组的班级组商，而这些子组由ramifeing Prime的类别产生的子组）。我们证明我们的猜想是tamagawa数字猜想的结果，并且还证明了我们猜想的iWasawa理论版本在假设$μ= 0 $的情况下是正确的，而无需假设ETNC。
In this paper, for a CM abelian extension $K/k$ of number fields, we propose a conjecture which describes completely the Fitting ideal of the minus part of the Pontryagin dual of the $T$-ray class group of $K$ for a set $T$ of primes as a ${\rm Gal}(K/k)$-module. Here, we emphasize that we consider the full class group, and do not throw away the ramifying primes (namely, the object we study is not the quotient of the class group by the subgroup generated by the classes of ramifying primes). We prove that our conjecture is a consequence of the equivariant Tamagawa number conjecture, and also prove that the Iwasawa theoretic version of our conjecture holds true under the assumption $μ=0$ without assuming eTNC.
