Timeline for Field of Definition of a Meromorphic Function
Current License: CC BY-SA 2.5
6 events
when toggle format | what | by | license | comment | |
---|---|---|---|---|---|
Jun 15, 2010 at 13:13 | comment | added | Boyarsky | The operation of dividing $f$ by the value $f(x)$ at a distinguished point $x$ does not commute with the operation of $\sigma$. So this proof is not quite right. Instead, writing $\sigma(f) = c_ {\sigma} f$ for all $\sigma \in G_K$, where $c_ {\sigma} \in \overline{K}^{\times}$, we see that $\sigma \mapsto c_ {\sigma}$ lies in ${\rm{H}}^1(K, \mathbf{G}_ m) = 1$, so $c_ {\sigma} = \sigma(a)/a$ for some $a \in \overline{K}^{\times}$. Then $(1/a)f$ is Galois-invariant and hence defined over $K$. | |
Jan 5, 2010 at 22:01 | vote | accept | H. Hasson | ||
Jan 5, 2010 at 22:01 | comment | added | H. Hasson | I changed it in the body of the question. Aha, I see. Oh, excellent. Wonderful. | |
Jan 5, 2010 at 21:47 | history | edited | Ilya Nikokoshev | CC BY-SA 2.5 |
correction
|
Jan 5, 2010 at 21:40 | comment | added | H. Hasson | Oh, darn. Of course that's what I meant. Up to constant. | |
Jan 5, 2010 at 21:37 | history | answered | Ilya Nikokoshev | CC BY-SA 2.5 |