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created: 2023-03-26T11:58
updated: 2024-04-16T21:03
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# Galois covers

![](2024-04-16.png)

![](2024-04-16-1.png)

Here $\Aut(p)$ are the automorphisms $f: Y\selfmap$ with $f\circ p = p$, i.e. morphisms over $X$.
Require $p$ to be a [finite morphism](finite%20morphism) and an [etale morphism](etale%20morphism.md).
In this case $\size G = \deg(Y\to X)$.
Any finite etale morphism is dominated by a Galois cover.