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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.
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