# Spahn the fundamental group and Galois theory (Rev #1, changes)

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Let $o$ be a Dedekind domain, let $K:=Quot(o)$ denote its quotient field, let $L/K$ be a finite separable field extension, let $O\supset o$ be the integral closure of $o$ in $L$. Then $O$ is in particular a Dedekind domain

Let for

$o\stackrel{i}{\to} O\to L$

$f:=Spec(i):Spec(O)\to Spec(o)$ be the induced map between the ring spectra.

Let $p\in Spec(o)$ be a maximal prime ideal. Then the ideal $pO$ in $O$ has a unique decomposition

$pO=P_1^{e_1}\dots P_r^{e_r}$

with different $P_i\in Spec(O)$

## References

• Jürgen Neukirch, algebraic number theory, I.§13.6

Revision on August 25, 2012 at 21:53:32 by Stephan Alexander Spahn?. See the history of this page for a list of all contributions to it.