Timeline for transcendental Galois theory
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 13, 2011 at 15:16 | comment | added | M.G. | On a second glance over the paper, my guess is that certain statements are meant as yet to be proved or disproved, rather than as true or false statements (especially considering the fact that the paper rather appears to be a draft). I guess I should have added a disclaimer in my answer, lol. Anyways, when I googled "transcendental galois theory", the only two meaningful results appeared to be that thread (without a real answer to it) and the aforementioned draft paper. | |
| Jan 31, 2011 at 11:58 | comment | added | Laurent Moret-Bailly | Well, in particular, it is claimed in this paper (Remark 1.6) that if $L$ is a proper subfield of $\mathbb{C}(t)$ containing $\mathbb{C}$, then $L$ is not isomorphic to $\mathbb{C}(t)$. Not a good sign. | |
| Jan 31, 2011 at 2:29 | comment | added | Pete L. Clark | Let me also say -- and here let me be careful with what I am saying -- that I have glanced at this paper before as well as others by the same author. The claimed results are interesting, but I've never been able to follow the proofs. | |
| Jan 31, 2011 at 2:27 | comment | added | Pete L. Clark | @ex falso: $\mathbb{C}(t)/\mathbb{C}$ is definitely not a Galois extension according to my definition. My definition of Galois implies that if $L/K$ is Galois and $M$ is any subextension, then $L/M$ is also Galois. Taking $M$ to have finite index in $\mathbb{C}(t)$ and applying Luroth's theorem, if this were a Galois extension then every finite covering of $\mathbb{P}^1$ by $\mathbb{P}^1$ would be Galois. But this is false: for instance there are well-known to be $A_5$ Galois covers of $\mathbb{P}^1$ over $\mathbb{P}^1$, and $A_5$ has non-normal subgroups... | |
| Jan 30, 2011 at 21:57 | history | answered | M.G. | CC BY-SA 2.5 |