Timeline for Given 2 towers of fields, when are these fields isomorphic?
Current License: CC BY-SA 3.0
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| Sep 7, 2011 at 17:51 | comment | added | Bill Cook | Many Thanks Francois! I should have been more careful when I posed the question. After @JSpecter posted his counterexample, I started to think back about my "proof" and realized I had been working in the context where $F_0=K_0=\mathbb{Q}$ (and all extensions are algebraic). I too would like to know when something like this holds (and get some references). | |
| Sep 6, 2011 at 11:15 | comment | added | François G. Dorais | The answers below give very nice examples where this is false, but the result is still true in some common cases. For example, the result is true when all the F's and K's are number fields. More generally, I think this is true if the F's and K's are all finite extensions of some base field and the embeddings are required to fix that base field. Are there broader circumstances where the result is still true? | |
| Sep 6, 2011 at 10:10 | answer | added | KConrad | timeline score: 12 | |
| Sep 6, 2011 at 3:20 | vote | accept | Bill Cook | ||
| Sep 6, 2011 at 1:06 | answer | added | JSpecter | timeline score: 14 | |
| Sep 6, 2011 at 0:53 | history | edited | user9072 |
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| Sep 6, 2011 at 0:31 | history | asked | Bill Cook | CC BY-SA 3.0 |