Timeline for Rationality of curve does not depend on base change
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| Nov 1, 2013 at 6:05 | comment | added | Pete L. Clark | That's a funny coincidence. Earlier today I wrote up a proof of the following Lemma: Let $K$ be a field and $L/K$ a purely transcendental field extension. Let $V_{/K}$ be a variety. If either $K$ is infinite or $V$ is complete, then $V(L) \neq \varnothing \implies V(K) \neq \varnothing$. The proof is not at all hard, but it becomes easier if you strengthen "complete" to "projective", as you note. Note that some hypothesis is needed to rule out things like $\mathbb{P}^1_{/\mathbb{F}_p} \setminus \mathbb{P}^1(\mathbb{F}_p)$! | |
| Nov 1, 2013 at 3:51 | history | edited | Abhinav Kumar | CC BY-SA 3.0 |
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| Nov 1, 2013 at 3:31 | history | edited | Abhinav Kumar | CC BY-SA 3.0 |
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| Nov 1, 2013 at 1:51 | history | answered | Abhinav Kumar | CC BY-SA 3.0 |