All Questions
Tagged with galois-theory covering-spaces
9 questions
3
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0
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Reference Request: Pushforward of $\pi_1$ along a covering map and the Galois group
Let $f \colon (Y,y_0) \to (X,x_0)$ be a finite-to-one pointed covering map. The pushforward gives an inclusion $f_* \colon \pi_1(Y,y_0) \to \pi_1(X,x_0)$. If we take the universal cover $\widetilde{X}$...
- 949
5
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To what extent are geometric methods being used to attack the inverse Galois problem?
My limited knowledge so far is that some groups have been constructed geometrically using the theory of covering spaces, then applying Hilbert irreducibility.
Is there a deeper way in which inverse ...
- 131
7
votes
2
answers
2k
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Monodromy groups from Galois's viewpoint
According to the Wikipedia article about monodromy, the monodromy group can be defined in terms of Galois theory in following way:
Let $F(x)$ denote the field of the rational functions in the ...
- 6,018
3
votes
2
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336
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English literature close to "Algébre et Théories Galoisiennes" by Régine and Adrien Douady
I'm currently working on my undergraduate dissertation. I'm working on covering sapces of Riemann surfaces so my supervisor asked me to read the book I mention in the title: "Algébre et Théories ...
- 133
13
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Actions of $\mathbb Z/2\mathbb Z$ on algebraically closed fields and even-dimensional spheres and parallel between Galois theory and covering theory
It is well known that there is a parallel between Galois theory and covering theory. So I wonder whether there is a deep similarity between the following two facts:
Artin-Schreier theorem. The only ...
- 1,980
3
votes
0
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155
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Making extensions $L/K$ aware of the Galois group coming from $K/k$
Although inspired by my question on math.SE https://math.stackexchange.com/q/1902190/214353 this is not a crosspost. What happened is that after an answer and some comments I realized more clearly ...
- 18.4k
6
votes
1
answer
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Geometric intuition for the condition of Galois descent
Continuing in my attempts to understand bits and pieces of Borceux and Janelidze's Galois Theories, I've just realized that I don't have any geometric intuition for the most convenient ...
- 10.5k
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Inverse Galois Problem ; Galois group of some branched cover of $P^{1}$ defined over $\mathbb{Q}$
I was trying to read a paper on Inverse Galois problem . I understands what the inverse Galois problem is. It asks if every finite group is the Galois group of some extension of the rationals.
The ...
- 591
9
votes
2
answers
939
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The holomorphic version of Galois theory
We identify the space of polynomials of degree n with $\mathbb{C}^{n+1}-\mathbb{C}^{n}$, that is an $n+1$ tuple $(a_{n},a_{n-1},\ldots,a_{0})$ with $a_{n} \neq 0$ is identified with $p(z)=a_{n}z^{n} +...
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