On the structure of ideal class groups of CM-fields.
For a typical example of a complete discrete valuation field of type II in the sense of [], we determine the graded quotients for all . In the Appendix, we describe the Milnor -groups of a certain local ring by using differential modules, which are related to the theory of syntomic cohomology.
In this paper, for a totally real number field we show the ideal class group of is trivial. We also study the -component of the ideal class group of the cyclotomic -extension.
Page 1