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Results tagged with class-field-theory
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user 4213
20
votes
$A_5$-extension of number fields unramified everywhere
Here's the standard example. I found it in Lang's Algebraic Number Theory
where he attributes it to Artin. Let $K$ be the splitting field of $X^5-X+1$
over $\mathbb{Q}$. Then $K$ has Galois group $S_5 …
- 41.4k
34
votes
Accepted
Shortest/Most elegant proof for $L(1,\chi)\neq 0$
I like the proof by Paul Monsky:
'Simplifying the Proof of Dirichlet's Theorem'
American Mathematical Monthly, Vol. 100 (1993), pp. 861-862.
Naturally this does maintain the distinction between real …
- 20.8k
5
votes
Is there a notion of Galois extension for Z / p^2?
There's the notion of Galois ring. Let $K$ be the degree $m$
unramified extension of $\mathbb{Q}_p$
and let $\mathcal{O}_K$ be its ring of integers. Then the quotient
$R=\mathcal{O}_K/p^n\mathcal{O}_ …
- 20.8k