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Results tagged with cyclotomic-fields
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user 5015
A cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to $\mathbb Q$, the field of rational numbers.
2
votes
class group size of cyclotomic field subextension
The $p$-primary part of the class group of $\mathbb{Q}_1$, and in fact all $\mathbb{Q}_n$ in the cyclotomic tower of $\mathbb{Q}$, is trivial for all $p$. This is contained in Proposition 13.22 of Was …
- 8,945
5
votes
Accepted
Splitting of primes in cyclotomic $\mathbb{Z}_p$-extension
For any $\mathbb{Z}_p$-extension the ramification is concentrated among the primes above $p$. Those that are ramified are totally ramified.
For the cyclotomic $\mathbb{Z}_p$-extension all places abov …
- 8,945