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Results tagged with function-fields
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user 6776
0
votes
1
answer
406
views
The image of generator under an automorphism of a cyclic function field
I'm reading the proof of Lemma 4.1 [1] which says:
"Let $F = K(x,y), y^q = f(x)$, where $q$ is a prime different from characteristic of $K$.
Let $Z := Gal(F/K(x))$ and we have $Z < G < Aut(F/K)$ Then …
- 601
0
votes
Accepted
The image of generator under an automorphism of a cyclic function field
OK, finally, I think I got it, but it is not that trivial to simply be omitted from the proof (If I complicated it and there's is a straight forward way to see it please tell me):
We have $\sigma(y)^ …
- 601
0
votes
Accepted
Computing the fixed field of an automorphism of a function field
Colin Weir, suggested the following algorithm to solve the problem in non-rational case, I thought for the sake of others who probably have the same question, I'll post it, here:
Suppose that $\sigma …
- 601
6
votes
2
answers
2k
views
Computing the fixed field of an automorphism of a function field
Let say we have a function field $k(x,y)$ defined by $f(x,y)$ over $k$, with $\sigma \in Aut(k(x,y)/k)$ and. Suppose, I'm not that out of luck, so that either of $\prod \sigma^i(x)$ or $\sum \sigma^i( …
- 601