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Feb 24, 2023 at 8:25 comment added Kapil On page 143 of this book Washington refers to a paper of Sinott to say "it is perhaps better to take norms" to define $C_K$. I assume that this means that this image is easier to compute than the intersection.
Feb 23, 2023 at 17:00 comment added KConrad Have you looked at Section 8.1 of Washington's book on cyclotomic fields? It doesn't directly answer your question, but maybe some of the information there could help, such as Theorem 8.2 and Section 4 of the tables at the end of the book.
Feb 23, 2023 at 16:36 history asked Kapil CC BY-SA 4.0