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Results tagged with galois-theory
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user 65
Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is, in some sense, simpler and better understood.
5
votes
"Understanding" $\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$
I'm far from expect in this topic, but here's my attempt.
First, and that's something quite straightforward, people want to study Gal Q (this is how I will denote it; this common shortcut is defined …
- 15.1k
4
votes
Accepted
Field of Definition of a Meromorphic Function
It is not sufficient that the subscheme of poles and zeroes is defined together over $K$, as the example of the function $(z+i)/(z-i):\mathbb P^1 \to \mathbb P^1$, defined only over $\mathbb Q(i)$, il …
- 15.1k
3
votes
Galois groups vs. fundamental groups
You might like the following formal statement. Consider the field F with Galois group Gal. Then (finite) unramified extensions E/F are in 1-1 correspondence with (transitive) actions of Gal on (finite …
- 15.1k