Publication details
Annihilators for the class group of a cyclic field of prime power degree II
| Authors | |
|---|---|
| Year of publication | 2006 |
| Type | Article in Periodical |
| Magazine / Source | Canadian Journal of Mathematics |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | Class group; annihilators; cyclic number field |
| Description | We prove, for a field K which is cyclic of odd prime power degree over the rationals, that the annihilator of the quotient of the units of K by a suitable large subgroup (constructed from circular units) annihilates what we call the non-genus part of the class group. This leads to stronger annihilation results for the whole class group than a routine application of the Rubin-Thaine method would produce, since the part of the class group determined by genus theory has an obvious large annihilator which is not detected by that method; this is our reason for concentrating on the non-genus part. The present work builds on and strengthens previous work of the authors; the proofs are more conceptual now, and we are also able to construct an example which demonstrates that our results cannot be easily sharpened further. |
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