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 Gal(K/k)-module. Here, we emphasize that we consider the full class group, and do not throw away the ramifying primes (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 the Iwasawa theoretic version of our conjecture.
|Number of pages||26|
|Journal||Journal de Theorie des Nombres de Bordeaux|
|Publication status||Published - 2021|
- Class groups, Fitting ideals
ASJC Scopus subject areas
- Algebra and Number Theory